Man, smiley face guy was only one who answered correctly. I will elaborate on all your questions tho...
1. You can not join as a single mother, (this is for all branches) you can give custody to someone else, and then get custody back later on though. The miltiary does have single parents, but as stated, all after they joined. (I had my duaghter 3 months after, while I had just started Tech School)
2. Finishing up your Associates will be nice, you can enlist at a slightly higher paygrade E-2 or 3 rather then E-1, while still only commiting for 4 years of active duty. (You need your BA/BS in order to try to get a commision/go officer that's the 4 year degree not the 2 year associates)
3. Deployment times vary. Air Force which has the shortest average time deployed just went to 6 months Air Force wide, with the longest deployments for Air Force being a year (can extend a little longer tho)
Army does a year-16 months Same as Marines.
Navy is a little wierd, and not only do they do deployments anywhere from 4months to a year, but they also have their time on the ship.
4. Only some national guard contracts help with student loans... but Active duty will help you further/continue your education with 100% Tuition assistance while you are in, and then your GI bill when you get out.
Hope all this helps, Good luck!