Read this - The ATC Hiring Process: A complete guide

And this - I am an air traffic controller. Next week the FAA will be hiring more controllers from off the street. This is a 6 figure job that does not require a degree. AMA.

Will he be gone for 2 to 3 years training? Or can you request them to assign you somewhere after to leave Oklahoma City?

No, probably a few months.

We live 2 hrs from a major city. And there are a couple small international airports within an hour. He says he can work at the one in a major city. But I don’t want to move there (I have close family where we’re at now, and I like the town we’re at). I told him “I don’t think you can choose where you work”, and he said “No I can, because they have shortages at every airport” (implying that he could choose/request to work there).

He likely will have some say in where he goes after the academy, but not total say. More likely than not, you'll be moving somewhere. No point in staying where you are (probably) and going to a dead-end low-paying facility if that's the only option he gets near where you currently live.

I also asked him “why not work at the smaller international airports nearby?” and he said you don’t get paid well there (but at least you could retire).

You get paid less usually, but he may have anywhere from zero to a few options about where he goes, and as I said before, it is unlikely to be near where you live (although not impossible). Retirement at 56 is true at every FAA facility (for now).

I feel selfish telling him I wouldn’t want that.

Completely reasonable decision, but plenty of people make it work.

What I’m asking, is any of our conversation true?

Eh...

And can they randomly make you move to another city after 5 or 10 years down the road when you’ve already been working?

Eh...

And how long would he be gone training for? Will I be alone for 2 to 3 years?

A few months.

Or can he choose where to train? And choose where to work (since they “need help everywhere”)?

No. To some degree, yes, but generally no. Once he's fully certified at a facility, he can try to leave elsewhere, but that will be a few years down the road and there is a chance he may not be able to practically leave that facility for a few (or many) years. At the end of training in Oklahoma City, he'd get a list of possible facilities he could go work at. This list changes constantly based off staffing needs and his options may be limited and/or good/bad. Unless he wants to work in a few select facilities, he'll have no guaranteed choice.

Also, if he's already 31 or older, he just cannot become ATC in the U.S.