Practically you can do nothing without the SSN. If you haven't applied for one, you have to do so now.
1. I don't know about your financial situation but just moving in from Africa, I guess you need to try to find any kind of job that will give you some income to start with. Your host can play an important role in your search for a job. Then after you can look into taking some diploma courses.
2. Yes you can open an account, check the nearest Bank of America - they are flexible with new immigrants. You need your passport and any foreign-issued card (visa, mastercard, american express) as an ID. Just pay them a visit and get more details about the documents you may need, and moreover, you don't need to put in large amount of money - just $30 can open the account.
3. You can only build your credit history if you have a job. There is this credit card (secured credit card) from Bank of America and many banks where you load the card with your own money and use it as and when you like. It's a good way to start building your credit history. Meanwhile you can check these websites for more information on how to build credit history:
http://www.howtobuildcredit.net/
http://www.quizzle.com/blog/2010/04/how-to-build-credit-from-no-credit-in-6-easy-steps/