I'm an attorney in Indianapolis and will try to answer your questions.
First, I assume that they are wanting to divorce, not that they are already divorced.
If he wants custody, he can ask for it, just as she can.
Once the divorce petition is filed, the court schedules what's called a provisional hearing about six weeks later. During that hearing, the court decides who gets temporary custody of the children and what the child support amount will be temporarily.
If your son has a stable job, a good place for the kids, a clean criminal history and has been actively involved in the kids' lives, his chances are very good. I would need to know more facts, though, about him and his wife.
Dads in Indiana get custody very frequently when they ask for it. Most of my male clients don't want to fight for custody, but of those who do, about 90 percent win it.
Joint legal custody works only if the parties get along very well, if they live right down the street from each other and can easily transfer the kids back and forth and easily make joint decisions on them. This is granted very infrequently because most people who divorce are divorcing precisely because they cannot do those things.
Hope this helps. Let me know if you have other questions.