AWAY the week before in Vegas and first SEC series against MSU the following week is also AWAY so yes, there will be a HOME series the weekend your wanting to catch a game. Takes time for the schedule to come out and for those itching for one, fall ball isn't even completed yet. The team isn't taking a bye weekend first weekend in March. Get your accommodations lined up, Horns will be playing.
That's going to be tough one (LSU travels great) and the last time they were here (pre covid), CDC brought in temporary bleachers for overflow. I was glad I was a new season ticket holder and at least got to see the Friday night game. That being said, you should be able to get some on the secondary market or through the ticket office as many people give their tickets back to the school to be sold. Expect GA or down the lines though. Maybe some under the roof. There are a number of people around me that exchange or give away our tickets to each other if not going. PM me a heads up about a week beforehand and I'll see if any are available.
edit: I've had my same seats (2 on aisle) for 8 (?) years now and I have NEVER met the guy (or gal) in the seats to my left.....different people there EVERY game, every year, as the people that sit there during different series bought them through the box office usually day of game. Dude has never been to a game. So those will probably be for sale too.