You have a misunderstanding of conservatives...
1) Every conservative I know supports a social safety net for the mentally and physically disabled, for the elderly, for people who find themselves in a short-term bind due to the loss of a job, divorce, illness, etc. They even support earned income credits for the working poor and in my case preserving the extended Medicaid access to the working poor.
Where we differ with progressives is we oppose income redistribution in the name of achieving income equity or wealth redistribution. We oppose entitlement programs which undermine work and promote dependence. Do a bit of research on what percentage of children were born into single parent families before we built our extensive entitlement programs or what percentage of children grew up in poverty. When entitlement programs begin to contribute to poverty especially for children, it is time to revisit them and figure out why.
2) Abortion is murder by definition when it is illegal. There are no honest biologists that would argue that life does not begin at conception. And murder is defined as the premeditated decision to unlawfully end a specific person's life regardless of their mental state.
If you want to argue, that abortion while murder is beneficial to society, that is the argument the the founder of Planned Parenthood, Margaret Sanger made. You might have your own reasons why babies should not be brought into the world, but it is important not to make a nonsensical one like "Abortion is not murder".
You might embrace, the Roe v Wade decision which argued that up to viability a woman's right to privacy took precedence over a baby's right to life. But notice the Supreme Court argued precedence of rights not the existence of rights for a baby at conception including that the baby had a right to life, only that its right did not take precedence to the woman's rights.
Meanwhile the viability/privacy argument that decided Roe v Wade has collapsed to between 20-21 weeks. At the rate current technology is advancing, viability outside the mother's womb could collapse to almost as soon as the baby is "conceived" within a decade as fetal transplants may offer hope to parents who want a baby and cannot conceive one.
Conservatism simply acknowledges that a baby has a right to life (consistent with the Roe v Wade), except conservatives disagrees with respect to when the baby's right to life takes precedence to the mother's rights. In New York State, a progressive state ideologically they considered giving women the right to terminate pregnancies past viability. If New York can promote its values, it seems only reasonable that other states can promote theirs.
Bottom line it might make you feel better to believe you have a "biological argument" in favor of abortion, but that argument is weak at best. It is better to stick to the "rights" argument, when does a mother have a legal right to kill an unborn baby. If a mother has a legal right to do so, then it is not murder by definition.
3) Your definition of conservatism is accurate but also obsolete. Most conservatives I know are more like me... "classical liberals". Classical liberals believe in that when the Declaration of Independence declared all men were created equal, it was an aspirational statement regarding their status as citizens of the country. As a nation, we should strive to eliminate all barriers that stand between all citizens enjoying equal rights as citizens. A second premise is that governments exist to protect both the unalienable rights of all humans as well as the contractual rights outlined in the Constitution.
Progressive liberalism is not particularly "progressive" or "liberal". "Progressive" would suggest moving toward the goals outlined in a country's societal contract. Instead, progressivism has morphed into an ideology built around some the concept of Nirvana. If in order to achieve this "greater good" individual liberties and rights must be trampled on, that is okay under modern progressive thought. If discrimination is necessary to achieve that dream, then that form of bigotry or racism is an acceptable price to pay.
So, let's look at two issues. Gay marriage and affirmative action. Modern conservatives (classical liberals) would see gay marriage as consistent with providing gay people the same rights as other couples. They may balk at the word "marriage" and prefer to call it a "civil union", but the idea is everyone has the same rights in the pursuit of happiness.
In contrast, affirmative action is a form of systemic racism that tries to fix past racist policies and achieve some sort of racial equity by using discrimination as a "tool for good". Progressives have no issue with this since it advances society towards their concept of Nirvana. Conservatives see this as a step backwards by promoting discrimination when the goal should be equality.
4) Where did you get your totally crazy view of conservatives towards immigration. As a conservative married to an immigrant, I strongly support legal immigration. I strongly oppose illegal immigration. I live in southern California where we see the devastation illegal immigration brings as Hispanic communities are being infected by Mexican cartels and the I5 corridor (including my town) is dealing with a rise in young Hispanic girls being sex trafficked). Minorities are the most adversely impacted by illegal immigration, while white elitist progressives take shelter in their gated communities.
Your whole narrative is wrong. Studies don't show immigrants commit lower crime rates than citizens, they show legal immigrants commit lower crime rates.
And most conservatives I know support tying the volume of immigration to unemployment rates. When unemployment rates are low, legal immigration with an emphasis towards merit-based immigration should be expanded and when unemployment is high, immigration should be curbed. Likewise, most conservatives I know support guest worker programs as long as those guest worker programs don't contribute to undermining wages of workers which they have done in the past in everything from programming jobs in Silicon Valley to crop picking.
https://www.npr.org/templates/story/story.php?storyId=123811962
5) With regard to success in America. You need to read several longitudinal studies on the subject rather than newspapers. Several studies done over a decade using income reporting to the IRS show that the majority of people born in poverty escape it.
So, if that is true, how come the poverty rate does not change much and who does not escape? Those are the right questions.
Let's start with the groups that "don't escape poverty". More than any other group, single mothers that fail to graduate high school and have children before age 21 are among those that spend a lifetime in poverty and their children grow up in poverty. 34% of single mothers live in poverty. That rate is 6X higher than for married couples. Let that sink in... then go back to your social safety net point and realize the more extensive the social safety net has become the more women have become trapped in it. We are beginning to build a cycle of poverty. The answer is "education and opportunity" but with failing public school system, that answer seems beyond reach. Yet progressive liberals fight school choice at every turn.
A second group that does not escape poverty are those with serious physical and mental handicaps. We should take care of these people.
A third group group are people that have destroyed their lives abusing substances. Having worked with this group in my past, I still have no idea how it can be fixed.
The fourth group are people who retire without savings or outlive them.
So, you have one group that is chronically poor and unlikely to escape poverty, but the vast majority do actually "pull themselves out of poverty" only to be replaced by "new" poor. This "new" poor group comes from four primary groups. The first are illegal immigrants, while exact numbers are hard to come by poverty rates among illegal immigrants appear to be twice as high as the US population as a whole. Want to drive down poverty in this country, curb illegal immigration and increase legal immigration.
The second group is "young" poor. Many Americans even people from affluent homes like me start out poor. I married in college and was lived in furnished apartment where I paid rent weekly. It took a few years to finish my education and begin to climb the economic ladder. I would argue this kind of poverty is both normal and healthy. I have never forgotten what it was like to live on peanut butter sandwiches, tomato soup (6 cans for $1), the watered-down milk (we cut it 50%), etc. But most young people escape poverty within a decade as I did, only to be replaced by the new generation of young people.
The third group are seniors as noted above. They were not poor their whole lives, but when people retire and lose their incomes they often end up in poverty if they outlive their savings. This is tragic and given the demographics of our country will become an increasing issue in the future.
The answer is not government, we simply don't have the resources to fix this problem... part of the answer lies in the return of the extended family. Where older grandparents provide childcare while their children work. Other answers lie in more part time jobs for the elderly to supplement their incomes and contribute to the shrinking work force.
The fourth group are those who experience personal tragedies including divorce, loss of a job, accidents, etc. Many of these people transition through poverty with few remaining there. This is one of the groups that the social safety net is intended to help.
But the truth is if you are able bodied, there is a job where you can earn above the poverty line. Having employed tens of thousands of workers in my lifetime, suggesting that someone who is able bodied and able to work cannot escape poverty is simply ludicrous. They might not understand how to do it... but that is something that can be fixed if they are really interested in "pulling themselves up their bootstraps". They may not have the skills, education, or intelligence to become wealthy, but there is a good paying job waiting for them if they know what to do.
As for being an exceptional nation... my grandmother, mother, wife, and daughter-in-law immigrated to America (from the Caribbean, Europe, Asia, and Africa, respectively) over more than 100 years, because we are an exceptional nation. My wife and daughter-in-law were talking the other day and they laugh about America's self-loathing. We are the country people around the world want to come to because we have so many good paying jobs. The last thing they want is socialistic government-controlled economy that squeezes the life out of job creation and taxes the people into poverty. We have immigrants at our company without college degrees that hardly speak English earning over $100K a year as skilled laborers, who cannot understand why we have entitlements for people that "can" work.
I think everyone supports "progress"; we just don't agree over what that means. Today's progressive liberal ideology is neither new nor historically successful at elevating standards of living.