Is it difficult to earn a degree while being active duty? How soon could I start school after AIT?

Difficult is irrelevant, you'll either make it a priority, or you won't. The Army, and college, has made it easier than ever to attain a legitimate, regionally accredited degree these days. Back when I first joined you had to go to night school at the education center and on the weekends. If you were in a unit like I was, you were gone too much to attend. Plus, you had to pay up front and get reimbursed and TA only covered 75% of tuition costs.
Now, the Army has a simple online portal. You find a college, the education counselor loads your degree plan. An online planner pops up showing you what courses will meet your degree requirements. You click a few buttons and you're enrolled. As for taking classes, we now have classroom, hybrid where you take some of it in class, and some online. There are online classes where you sit and watch a lecture. There are ones that are completely self paced. There are ones where the entire course is on a thumb drive and you complete the work and mail it back, all completely offline. In the Army today, if you have time to watch TV or play video games, you have time for class.

How long should you wait? I would say about a year or less after getting to your first duty station. Long enough to know a little about your job. You'll never really know your whole job. As soon as you do, you'll get promoted or moved and have to learn that job.
You can pick any college, for the most part. Definitely pick a regionally accredited college. Your education counselor will almost always steer you towards one of the colleges on your post. I suggest Coastline Community College for your associates and then transferring to a bachelor program after that. There are multiple reasons why this is a better choice for you, but that's another conversation. In the end, it really doesn't matter what associates program you pick because they are all low level classes and most of them are general education and electives. CCC will also give you up to 40 Semester Hours of military credit in your degree program. That's two thirds of your degree.

Biggest mistakes-
1. Waiting till you get out of the Army to go to college on the GI Bill. Thinking it will be easier when not on active duty. Thinking the GI Bill housing stipend will provide enough money not to need a job.
2. Waiting too long to begin. Most people wait until they are trying to earn promotion points or become a Senior NCO to earn their degree. Either they are trying to make more points and get ahead of their peers for promotion, or they are close to retirement and want their degree completed before then.
3. Being enrolled in a degree program but not taking a course because of upcoming training events. As I said before, you can be completely offline and take a course. There are plenty of training events that last a month where you will be really busy, then have hours of down time just waiting. Even if you don't, you can request a course extension. If you wait until the training calendar is clear, or you're not already busy, you're going to lose a lot of good opportunities for courses.
4. Waiting for any sort of "right time". There will literally never be a right time. Especially once you have dependents, there is no extra time. You just have to make it more important than the other things in your life like going out on the weekends or entertainment. People find time in their busy lives for church every Sunday because they make spiritual development a priority. Self development is equally important.
5. Letting TA go unused. You get a limited amount of TA a year and that pot resets every fiscal year. If you don't use it by the end of the day on September 30th, then it's gone and the limit resets for the year.

If you attend just one class at a time for the year you will attend enough to be able to apply for FAFSA at least as a half time student. If you use your FAFSA money for more courses you could bump that up to three quarters. One to two classes at a time will allow you to maintain a high GPA and progress steadily towards your degree with no money out of your pocket. In the future you may want to apply for degree commissioning programs like the PA program, Nursing program, or Physical Therapy Baylor program, or even just OCS. Having a high science GPA and overall GPA will make you more competitive than your peers and give you a better chance at getting selected.

It can absolutely be done. It will obviously take longer than if you were going to school full time. You get tuition assistance one year after completion of AIT (meaning Army pays for your classes). But you can take CLEP tests (and get CLEP study material) for free as soon as you get to duty station.

You can pursue whatever degree you want, there are no limitations. However note that a degree that nests with your MOS may be quicker and easier because you may be able to apply military training and experience to some of those credits.

Mission comes first, though. I highly recommend doing one course at a time. Most posts are affiliated with a local U and will have accelerated 6-8 week courses. If you do those one at a time, but do it year round, you can knock out a semester (15 - 18 credits) a year. Again, not as fast as a full time student, but half speed for free while holding down a full time job ain't bad. At that rate, with the credits you already have, you can probably have a BS in about 6 years or so.

WAY BA k, there used to be Commander's initiative for a "college drop" as part of re-enlistment, where you would go to school full-time for a semester. Usially still had to do PT and things like urinalysis or PAI, but other than that, your duty location was college. Don't know if that is still an option, but if it is, that could also speed you up.

Depending on your unit, their OPTEMPO, deployment phase, training schedule, etc. You may be able to do more or less. But start with one at a time and see how it goes.

The two biggest mistakes I saw were kids going too fast or too slow. Either they were jumping in and trying to do too much and spreading themselves too thin (both school AND work suffer). Or they were putting school again and again because they were "too busy" with the Army. (I was the latter - I didn't get serious about college until I had been in for 16 years.) Slow and steady wins the race, here. One at a time, but ALWAYS (or almost always) be taking a class.

Honestly how easy it difficult it can be is entirely up to you. It's about the effort and work you put into getting your degree. Even with deployments there's still a way to get the work done, all be it a lil slower while deployed, but none the less still achievable. Just give yourself a small goal when u first start then when u reach that goal move to the next bigger one each time until complete. Hope that helped despite the long winded answer.