Yes, I do it all the time. In fact, I find it much easier. If you are worried about runny mixture, encase the underside of the tin in foil, which will stop any excess running over your oven.
Yes you can but I suggest using a sheet of wax paper on the bottom so you can remove the cake from pan bottom easier.
Yes, but you need to line it with baking paper/parchment ( not the same as greaseproof paper, but a combined paper of both is suitable). Place a tray underneath as it may drip a little. I use them all the time with no problems.