Hi. I'm LDS (Mormon) and could tell you anything you want to know about it. All my brothers served missions. If your stepson is Mormon, he probably will want to serve a mission (a norm for LDS boys). It's true that when they go there are pretty strict "rules" about contact with family. They do this so the missionary can focus on the mission and serving the people there rather than worrying about friends and families back home. Everyone I know who has served has said that it was hard at first, but actually really helpful to them for that time. It's especially easy to be homesick when you live in a totally new culture with complete strangers, and phone calls and visits from family doesn't actually help.
You can write, send care packages, email, etc. You stepson would be able to write you (or email, depending on where he serves) and send packages as well. He can also call you on Christmas and Mother's Day (or in an emergency or something).
It's always really hard for a family to send a son (or daughter) away for a while knowing you can't see or talk to them regularly, but it's an incredible experience for the missionary. Whether you agree with the church aspect of it or not, the skills and growth a young person gain from it is incredible.
You mentioned that he's being "pushed" to go. Obviously I don't know the situation, but I'll just offer some inside perspective for you on that. Of course sometimes boys are pushed to go, and everyone is going to feel differently about how much "pushing" is appropriate (not much, in my opinion, but that's just me). But you have to realize also that if he is Mormon, and intends to continue to be Mormon, he probably really wants this for himself. It's almost a rite of passage for Mormon boys, and he is probably aware that he would be missing out on an experience all his peers had if he chose not to go. It's also something girls pay attention to, which will be a big deal to him.
On the other hand, if he really doesn't want to go, I would hope and expect that his local leaders would pick up on that and not send him off. They do have a pretty high standard about who they will send, and they want to make sure a young man has his own motivation. I personally really believe it should be a personal choice (but within the church, it's a bit like choosing whether to go to college. A parent would certainly encourage a kid to do it. And some kids need encouragement to point them in the right direction, whatever that is). Again, I would stress that regardless of whether you agree with the church or its teachings, it's an incredible experience and opportunity for growth for him, so I wouldn't worry too much.
Good luck! I'd be happy to give you any more insider info if you want it.