In my case, all those UI issues were fixed by the day one patch. Just let Steam do its thing, update the game, restart the PC and try again. Now here's an evil thought, maybe it's creative DRM on Beth's part, like the Rocksteady Batman cape glitch that hit pirate copies.

Also, re: mouse lag, edit your ini file to disable vertical sync, that's what's causing it (and also slowing down your frames). Check out tweakguides.com for details (and stay tuned for their in-depth guide to squeezing more performance out of the game)