I am studying at a law school in my home country. I am interested in applying for LLM in the USA but I have no work experience except legal internship during my undergrad years. I have questions and thank you for all your help!

1.Any universities that I can apply if I have no work experience?

2. What are the Prospects for foreign lawyer's employment after LLM from American law school?

3. If I pass the NY bar exam, Will there be more chance for a job opportunity?

Every LLM program in the US has its own approach to admissions and prior work experience. As your question suggests, there are some programs for which one or two years of work experience is a prerequisite for admission. However, there are many programs that, while they will consider work experience as a part of the full record, will happily admit a student who has just completed their first professional degree abroad. Here at Pitt Law, and at a number of other law schools, our LLM classes have included both students fresh out of their LLB equivalent and students who have been in practice for many years in their home countries.

Regarding your second and third questions, if you are asking about an LLM graduate's prospects for employment in the US -- while I know of a number of LLM graduates who have been able to use the degree and a US bar admission to gain employment in the US, most LLM graduates will return to their home countries or regions after their degree year (and perhaps an internship of a year or less on OPT). I would not recommend seeking an LLM for the sole purpose of obtaining employment in the US - remember that, even with admission to a state bar, you will be competing in a very tough employment market against US JD graduates who (a) have the advantage of three years of training in US law versus one and (b) who in most cases willl not present a potential employer with the costs and uncertainty associated with sponsoring an LLM graduate for a work visa. I think that the LLM is a terrific credential and experience, but long-term US employment should not be your primary objective in seeking the degree.*

*With this exception: Every year, there will be at least one student in my LLM program who is committed to live indefinitely in the US because of a relationship, refugee status, etc. - for them, it absolutely makes sense to pursue the LLM as a gateway to US legal employment, although we will discuss with these students as well the challenges of the market and the potential benefit of a JD degree (either from the start or as an LLM-to-JD transfer student) for their employment prospects.

Answer to your questions.

1. There is always some school willing to take your money.
2. The better the pedigree of your school + your past work history + your home country country ties + anything that might increase your value in the market place, increases your odds of getting work a job after you complete your LLM. As mentioned your are competing against JDs and are at a distinct disadvantage in the market place. So usually unless you can offer something very unique/compelling to an employer in the US, there is little benefit for them to employ you. But maybe you are from China and speak Mandarin and Cantonese and you have very good connections back home, then they may employ you for a time to develop a relationship with you and when you go back home you can be an asset for them.
3. It can be helpful depending on where you are trying to get in so to speak. There are lots of lawyers in NY already. It will show at least some level of proficiency though. Even then I found many employers wouldn't consider me without a JD even if I had passed a bar in the state they were in.

Overall tip for getting a job in the US. Go to the best school you can even if it costs you more money. The caveat to that is if you are looking at 2 schools very close in ranking, it might not make much of a difference then. But if I had to pay to go to SLS or could go for free to Boston University, I would pay to go to Stanford! I might rethink that a bit though if the school was very strong in their local market and there was a firm I was trying to get into based in the backyard of that law school so to speak.