I just did this for the first time and the batter pretty much just slopped down the pan and to the bottom of the stove. It made a little of a burnt smell (the stuff on the bottom) but now it's not smelling burnt anymore. Is this okay? The cake that's in the actual pan looks fine and isn't messed up looking (from what I can tell).

I was aiming to fill it enough so that I could level it while in then pan but I guess I went too far.....

It could be okay or not! You'll find out if you are torting the cake. Overfilling does tend to make a cake heavy as cakes need room to rise and when there is none you loose texture from the overflow.Next time you can just put a collar(with baking paper or brown paper) round the pan to maintain the height you want.

It should be ok, I started placing a sheet of tin foil on the rack below my pans for that very reason, if it overflows, it hits the foil and not the bottom of my stove were the burners are and keeps it from smoking.

Most likely it's fine.