A lot of good questions in this post. I'll try to answer them all, but I may have to break my post up into smaller posts.
First, I haven't been to San Antonio since I was an all state tuba player, but I know TMEA is a massive week for HatM and Pat O's. Cover is probably increased during that week but most places charge between 5 and 8 dollars.
All four pianists split tips evenly. As far as the show goes, we take turns playing one song at a time, and we have a thing called "pacing" where we try to break up the constant stream of songs with "bits," like call downs, shot toasts, crowd splits (assigning parts of a sing along to the two halves of the crowd to pit them against each other), and other comedy type things. So, we split the show evenly as well as the tips.
We here in Lubbock have four pianists, and we all play across from each other on different nights. For example, a plays with b on Thursday while c plays with d. A plays with c on friday, then a plays with d on saturday. So we play with the same group of guys, but not the exact same guy every night.
Roles during the show itself aren't a big deal, we all provide the same amount of work with piano and singing. During the change overs when teams switch out, we all play different instruments. I play fiddle and trumpet, so when we do "The Devil Went Down to Georgia," I'm the guy for that.
We practice the songs when we learn them, but we don't really practice them much after that unless we learned something incorrectly. In the moment, there is a sense of predictability that keeps us comfortable with each other, but it's sort of improvised in the sense that we do things differently sometimes.
We don't use iPads but some places do. I think it's kind of a bad thing to do because we need to stay connected with the crowd, and reading lyrics takes that away. We memorize everything we possibly can. On slow nights we might pull up lyrics on our phone but it's not a habit.
If we don't know a request we either address that we don't know it, play something else by the same artist, or offer their money back.
We have the billboard.com top 100 up on the computer just about every night. We have to learn all the crap in the top ten whether it's good or not, because it will inevitably be requested. Taylor Swift has grown on me a little, but not Nicki Minaj.
The dueling piano bar is my only source of income aside from playing gigs with my jazz trio. I make roughly 30k a year. Tips add about 5k a year.
It sounds like you have a good enough skill set to do this job if you wanted. We are always looking for guys who can play and sing even a little bit. Just saying.
My personal strengths come from being a jazz musician, a composer, and possessing the closest thing to perfect pitch one can learn. When I practice for work it's usually figuring out chord progressions, then learning lyrics, then drilling those until I can't forget them.
I don't have time to give you a full song list right now, but if you're still interested by tomorrow I can post a list. Thanks for all the great questions, let me know if you want to know anything else.