G.B.
1. If you had pullups on his you would have no accidents to clean up. Their purpose is to protect your furniture and flooring from this. They work like underwear because they are easier to push down and pull up.
No, he's 2...not 10. He should not have to clean up anything, he's learning so it's not his fault he pees on your floor, it's your fault for not taking him in time. When it comes right down to it the choices YOU make are what makes the accidents, he's still working on walking and talking at the same time, peeing in a potty and learning what that feeling is, if he even has it yet, is a lot to add to that.
2. Dump and rinse. Seriously, do you clean your toilet after each use? No, you flush it. Occasionally you clean it. Same with a potty seat.
3. Give him 1 jelly bean for pee and 2 jelly beans for poop. Or M&M's, what every small candy he loves. It has to be a treat though. Not something he ever gets any other way.
4. Use pull ups. No issues. Take him to the bathroom as soon as you get there and then while you're there if it's more than an hour.
5. Always have him sit backwards on the big toilet. It prepares him for standing and facing the same way, he can't fall in this way because his legs are totally supporting him. No worried or issues.
6. He's young for this so be patient. Make it fun, it goes much better.