This process is not geared toward foreigners; with no social security number or U.S. credit history, you can't apply for a conventional mortgage in the usual way. These days, it's difficult even for native students. A typical student has low income and high debt, yielding an unfavorable debt/income ratio. He surely has a short credit history as well.
I've sold to foreign students before (mostly Asian, but one from Iran). The most common way to do it is cash. Pittsburgh is very affordable; you can get a starter house in move-in condition for $30k-$40k in many areas. If a loan is necessary, the most common way to do that is to borrow against *other* property (e.g., their own home in the home country, if that's possible). Or some combination of the two.
For instance, one student bought a house in the city for around $105,000. The student was able to borrow $45,000 or so, but no more. (You can't get a regular mortgage for under $40k anyway.) Her father gave her the rest in cash, using a "gift letter" from the lender. That was a graduate student who'd been here many years, though.
I also have some experience with qualifying buyers who have a U.S. credit rating but substantial assets overseas. This is difficult, but not impossible. The main problem is the language barrier; you need certified translations of all documents. And sometimes the type of document you need here might simply not exist in the foreign country. I had a big problem getting an employment offer letter from Japan once; they handle that very differently, and cultural factors make it extremely difficult to get a letter with, for instance, the salary stated explicitly. There can also be tax issues. In Italy, someone once estimated that if all nominally due taxes were paid, they would add up to 104% of income. Nobody wants to write their "real" income down for fear they'll get taxed more :-)
Anyway, it's not easy as an undergraduate. One option would be to rent for a couple years while you get a SS# and build up a credit history. Paying rent and utilities (phone, Internet, cable, gas, electric) regularly helps, as does any sort of installment debt. You can get a credit card and use it for everything (very common in the U.S.; rare outside). As long as you don't spend more than you can pay off in full each month, it won't cost anything to do this, and it's very convenient. You can see all of your spending on the monthly statement, and use that as a budgeting aid.
Once you establish a credit rating and have some regular income, you're in a position to buy. If you still need help, your parents can gift money to you (possibly borrowed against different property or something else). Good luck!
Your parents can purchase a home for you in the USA. There are no citizenship restrictions on property in the USA.
The sellers will want to get funds through a US bank. Your parents will need to explore whether they should finance with a US institution or your home country. I recommend that you discuss your circumstances with a mortgage company and find out whether they have experience with foreign owners.