self-employed, limited credit history, been outside the us, do I have hope?
Since you're currently self employed, you must show the lender 2 years self employed history and proven income in US. Also you will have establish your credit once again, which also take few years. So at this point you will have to wait.

Why would anyone do a 15-year fixed mortgage?
The rate will be lower and you will be able to pay your mortgage faster, which means you will save a lot on not paying extra interest.

What is a better choice a 15 or 30 year mortgage for new home?
If you can manage 15 yrs fixed options, it always the best option. The rate is lower, thus the interest you will end up paying will be less.

My first home purchase question
You don't have any other options, but FHA when you put 5% down for a condo. PMI will be automatically obtained by the lender, your monthly PMI will be around $79 dollars. My suggestion if you can afford buying and be in your own home, it is always better the renting. You get to enjoy your own home.