Community colleges are not bad to get a start on your degree. There's no EARTHLY reason anyone should pay 4-year college prices to take stuff like "College Algebra 101" "Biology 101" and all those other things that are college requirements. Being from another country, there's no real telling which of your courses will count for American college credits, and which ones won't. I graduated from high school, assured that I had completed all the requirements to enter the local university....and it turns out I lacked about 3 courses. And my high school and college are in the same town!
The quality of education you get at a community college, to me, is kind of irrelevant if you're not planning on staying there to get a degree. The curriculum at a community college is either accepted by 4 year universities, or it isn't. Personally, while community college courses aren't as high-falutin' as 4-year college courses, they're adequate based on my experiences. They are geared for people who want to start working sooner than later and are often just trying to meet the bare minimums, but they give you the fundamentals. And again, if you're going to a 4-year college, the absolute quality of education you're getting at a community college is kind of unimportant compared to the next 3 to 5 years of education you're going to be getting at a 4 year university. It's kind of like sweating having a bad driving instructor when trying to get your license. Having a bad instructor for the 30 minutes they're in the car with you means very little compared to the next 50+ years of you driving. As long as you passed, that is.
So. Your parents are....half right. You can get a degree at a community college that is perfectly fine for lower-level stuff, accreditation, ect.... but if you want that full on Bachelor's degree or anything higher, you'll want a 4 year university.
Community colleges can also be helpful for adjusting to the rigors of college courses. Sort of. Sometimes. They tend to be slightly less intense than your average 4 year college.
If money is no object to your parents and you feel equipped to start a 4 year college, just go to a 4 year to start with. If you and your parents are interested in saving money and you don't mind the extra hassle that transferring schools, getting your transcripts sent, ect... presents, a community college is a decent place to start.
On the other things, sorry I'm not a lot of help on those. I have no idea what challenges someone faces trying to go work and go to school on a certain class of Visa.