Will the Ph.D. stipend be enough to support my parents?
- I estimate that I need to send about 400 USD a month to my parents. Will I be able to afford it?
I live on a graduate TAship that pays slightly more than 20K per year. I can put away about 200 USD every month. I live in a fairly expensive city, eat out once or twice a week, but don't have a car. Exactly how much you will be able to send home will depend on your lifestyle and where in the US you live. New York? You'll probably have very little left over. Middle of nowhere, out on the coutry? 400 USD is reasonable.
- Am I correct in assuming that the typical USA stipend would be about 20K a year?
Depends on your subject area and school. Some have more funding for grad students, others have less. Your advisor may also be able to supplement your salary from his grants if he's well-funded. (Bur yes, somewhere between 18 and 25K are the most common figures).
- Will I be violating any terms of employment of the university, if I take up part-time employment during my Ph.D.? What is the typical nature of part-time jobs one may find? Is it worth it?
Typically, you will have a TA-ship which will count as your part time job. Most schools require you to get special permission to have additional jobs, and these permits are very hard to obtain. In addition, a PhD is hard. You won't have time for much more work outside.
- Is one eligible to seek part-time employment under F1-visa (I am assuming that is the typical student visa)? If not, what are the other options? Are the other visas significantly harder to obtain?
You can only work for up to 20 hours a week during term-time on an F1-visa. These 20 hours have to be on campus, and typically your department will report your TA hours as your work hours. This effectively prevents you from working extra during the semesters. During holidays you can work for at most 40 hours a week, on or off campus. As a student, you need to be there as either an F1-student, or with permanent residence. Permanent residence is orders of magnitude harder to obtain (pretty much impossible).
- Are graduate school stipends taxable in the USA?
Depends on the state, and if all of it is payed out as a scholarship, or if some is payed out as a salary.
Just to add my personal anecdote to illustrate that this can easily be done.
I was a graduate student at Ann Arbor, Michigan. My stipend (or rather pay) came to less than $2,000 a month after taxes (during the 8 months of the school year). The pay package fortunately covered any tuition expenses and also health insurance - I think though that this is pretty standard anywhere in the US.
I was nonetheless able to save well over $1,000 per month, even without making any effort to do so.
My monthly expenses were usually just $500 for rent (plus all utilities, including internet) and another $200+ for food. I always had my own private room. Food was mostly just groceries, with occasional eating out. Anything else I treated as a luxury. For example for transport, I simply had a bike (≈ $130 off Amazon) and for my cellphone I just had a prepaid one (you can pay $100 for a cellphone that has something like 1000 minutes, 1000 texts loaded - this can easily last you a year if you're careful). The cost of living in Ann Arbor is probably slightly higher than the US average, though certainly lower than NYC or SF.
So I'd say yes, saving $400 per month is easily doable, if you're prepared to live a lifestyle that is considerably more frugal than what the typical American is accustomed to. And it sounds like you are indeed prepared to do so.
Note that legally speaking, if you're a dirty foreigner (like I was), you're legally allowed to work only 20 hours a week during the school year. So if you're already a TA or RA, it's likely that you cannot legally work any more hours. However you can still find freelance and lucrative work, e.g. tutoring undergraduate students. This is technically illegal but it's unlikely you'll ever get caught (many foreign grad students work off-the-books but I've never heard of anyone getting caught).