Do grad schools(not med schools) care about citizenships?

I was thinking, these days undergrad education is de-facto “required” education for all US citizens, so they do and should prioritize US citizens/PRs. However, grad schools are entirely by choices AFAIK.

Does international student status negatively affect grad school admission as much as it does to undergrad admission?
Also, are they allowed opportunities to be TA or test graders to partially pay for masters/phd cost?

What kind of grad school? From what I can see, there are plenty of international PhD students, especially in the sciences.

I am talking about in general, but if I have to be specific, chemistry or chemical/biological engineering.

There may be unconscious bias, but really, no. They want the most promising.

^ I am not convinced that that is true. Funding at least seems to be tied to immigration status in some instances.

When I was applying to PhD programs in math, one department (at a public university) first rejected me and later admitted me, with a fellowship offer nonetheless. Confused, I asked what had happened. The graduate chair said that my application had accidentally gotten into the international pile and the department has very limited funding for international graduate students.

I did not ask for further details at that point, but I am guessing it had to do with eligibility for in-state tuition rates. The department warned incoming US citizen/PR graduate students that they would only fund out-of-state tuition rates for 1 year, and that students were responsible for taking all of the necessary steps to establish eligibility for in-state status. However, international students would never qualify for in-state rates, which makes them much more expensive to fund.

As another example, I had an international friend in college who wanted to study aerospace engineering in graduate school. She got rejected everywhere she applied, and multiple programs told her specifically that that was because she was not a US citizen (restricted funding some places, concerns about national security conflicts causing her student visa to get denied elsewhere).

What if I don’t have to worry about money?

The type of visa you are on will matter. As said in #4, a particular program may not have room for an international student because of jobs required with the program like an internship at NASA or another agency. Those require citizenship.

Foreign students can attend law school, but where will they practice?

I think there are plenty of programs that will take foreign students, you just have to find the one you want that doesn’t have a restriction.

OK, yes, there may be funding issues as well.

Are you talking about Masters or PhD?

Masters. I don’t think I am dedicated enough for PhD…

OK, in that case, there is typically no funding for anyone anyway and schools likely won’t care what your citizenship is.