Is 50 minutes layover enough time for my checked bags?

Shouldn't be a problem and even if they miss the flight the airlines will get them to you on a later flight and time. This is one of the reasons that when I used to travel a lot that I always put things such as personal hygiene, medication and a set of clothes or a uniform in my carry on baggage, one does however need to be mindful in this day and age of what is allowed to be carried on by TSA.

Should be. You need to know how the system works nowadays. Bags go off and are tossed on a conveyor. Bags at destination go to claim. Bags are scanned and routed on belts to whatever location your next flight is. Difference and distance between airlines doesn't make much difference other than getting diverted on a few more belts and about maybe 3 more minutes. Final scan is to the cart that gets pulled out to the plane. They know if your bag isn't there, hence you'll hear the "we're waiting for a few more bags" thing about half the time. Final few scanned and loaded and they absolutely know your stuff is aboard. Airlines really do work to get your bags with you as their cost otherwise is significant. But that didn't make us feel better when we flew from Adak, to Anchorage, to Seattle, to Burbank and our dog didn't make it. He showed up in the back seat of a Yellow Cab later scoring a pastrami sandwich along the way. So stuff happens.

If it is the same airline, that is plenty of time. If not, and your bags don't make the connection, the airline will deliver to you. Just go to baggage rep at San Antonio and fill out he form.