Sorry for the late response, I'm not on here as much as I used to be. Hopefully you still see this.
1. DSLRs have a 20-30 minute timer limit. Once that amount of time has passed the camera will stop recording.
2. I personally prefer the tripod setup off the table so I can see the whole entire timer and myself. But this method requires more time and sometimes space doesn't allow for it. Thats why I've been doing table cam recently. The comps I was at didn't have enough space. But when I do table came, I just set it towards the edge of the table and focus on the cube cover/stackmat.
3. Neither personally. The problem with auto is that the camera might decide to expose for the light behind you which would make you really dark. So what I would do is just use manual and set your exposure settings so that you look bright enough (which means the background will likely be blown out). I always use manual for still images and pictures. Auto typically doesn't do a great job, especially auto focus. Auto focus in DSLRs is absolutely terrible, so I always use manual focus and set it to the cube cover or timer. I've found that focusing on the stackmat works best because typically my hands are behind the timer or right above it when solving. If you focus on the box the cube will likely be slightly out of focus.