So, again, quite a bit to unpack here, but as a general statement you have been lied to quite a bit. Virtually every point you made is a common myth promulgated by vaccine deniers.
It is factually incorrect to say that the US has more vaccines than any other country on its schedule. Australia (for example) has precisely the same schedule, with a few minor differences, mostly in terms of timing of certain vaccines. Different regions of the world differ slightly in their vaccines — for example, not every country has endemic Hepatitis B, so some don’t vaccinate for it routinely — but most OECD countries have a very similar vaccine schedule to the US. Check the link above if you don’t believe me.
Then, compensation. My main point was that US law notwithstanding, if vaccines were injuring kids you could sue in any other country in the world. Let’s say German kids were being harmed in record numbers, as you claim US kids are. Their vaccine schedule is virtually identical to the US. They use the same vaccines, made by the same companies in the same way. Why are German parents not suing these companies in droves? What about Australians? French? Etc. You don’t see millions of civil suits each year against vaccine manufacturers in all these countries, despite the fact that they use the same vaccines. It means that the vaccine court legislation in the US — which by the way does not prevent you from suing vaccine manufacturers that is also a lie you can read the legislation here — has literally nothing to do with vaccine research and/or injury.
As to how often serious adverse events happen: you mention the vaccine injury compensations. Here is the data on how many compensations are given per vaccine. As you can see, it’s about 3 thousand compensations for 3 billion vaccinations. That’s about 1 compensation per million vaccines. When you look at studies of millions of children, you find similar results — every million or so vaccinations causes 1 severe problem, most commonly anaphylaxis but occasionally other systemic immune issues.
In terms of studies comparing vaccinated and unvaccinated kids, again you have simply been lied to. There are plenty. Those who claim different are just factually wrong.
As to your last claims, around how healthy young kids are, you have again been lied to. Kids are at this very moment the most healthy that they have ever been. There are more chronic conditions — such as asthma — but we have driven infectious disease down to almost nothing. For a quick and easy look, I’d refer you to the graph below:
Here you can see death rates for infants, neonates and postneonates. The trend is abundantly clear; in the US, kids are getting healthier every year.
And you know what? A lot of that is thanks to vaccines.