Yes, you can vinyl plank straight over tile. I did it for a bathroom and it turned out great.
As far as leveling, unless we're talking something massive, I'd just buy a decent waterproof padding. It should cover most of the imperfections. This assumes the floor itself is level. If it's not, you'll need to add some floor leveler first.
To finish the room, I ...
The imperfections will be felt through the vinyl flooring if you do nothing.
You should remove any tiles whose edges are not flush; hammer them, chisel them, whatever.
Next you should pour self-leveling cement and sweep it into all of the grooves. Now you can install the vinyl.
Remove all of the tile until you get to the flat sub-floor ...