Is it possible for an international student doing JD at a T6 school to do SA for both 1L and 2L summers? My understanding was that international students on F-1 visa can work for 1 year max before graduation on Pre-Completion Optional Practical Training approval, so if I do 1L SA, I would use up that 1 year period before the 2L summer. Does anybody know how I could work my way around to do SA for both summers?

Also, does it happen often that international students with full-time offers at law firms after graduation get citizenship or green card?

You should be using CPT instead of OPT for your summers. That way you can save your 1-year OPT for after graduation. The international students office at your school should give you all the info you need about how to apply for your CPT and it usually only takes a week to process.

CPT is best because then you don't use up your one year of OPT. If not, you can still use OPT, you would use 3 months the first summer(pre completion OPT is time limited, its not 1 year all in one go), 3 months the second and still have 6 months left to take the bar. Keeping the full year OPT for the end is better because if you don't get an H1B for the October after you graduate(because they are all gone for example), you can use the cap gap to keep working. If you only have 6 months left because you used OPT both summers, your OPT would expire in January, and you can't file H1B petitions until April, so you would be out of status and have to leave until October(not ideal in your first year as an associate). 9 months might JUST get you there, but better to have the whole year to be safe.

Getting a green card will be VERY hard, although it will depend on what country you're from. It can take up to 6 years, requires the company to agree to sponsor you and if you change jobs your entire process starts over again. Citizenship you would probably only get through marriage.

I'm a T6 international student that did an SA last summer and will be starting at a firm in the fall. PM me if you have more questions.

EDITING to add: If you're talking about this summer it would be way too late to get OPT anyway. CPT would be your only bet if you're doing your 1L SA this summer. If you're not then I'd worry about the immigration consequences of getting an SA both summers after you get to law school bc its very very unlikely.

getting a law firm/law company to sponsor you for a work visa will not be that difficult.

a greencard is a matter of time.