A piece of help (others, don't hesitate to correct if needed):
(to) jump: tonde! (iie iie, joudan ;-))
(to) sneeze: ugokuna!
(to) lay down: don't know...
(to) roll over: gurugurushite (tadashikunai kedo, kawaii
)
(to) heal/beg: don't know...
(to) shake butt: buriburishite?
(to) shake hands: akushuu! (not sure about the spelling here)
Plus some more I think you could use:
(to) drink: nonde
Stop it!: yamete!
Go!: ikke!
Die!: shine! (er...well, sorry, it's not that kind of game LOL ;-))
Dance!: odoroke!
...I don't have more in mind right now. If you find other funny tricks for your dog, don't hesitate to come and ask here, OK?
Ha, and by the way, "osuwari" is best for saying "sit" to a dog...and in reverse, -never- say "osuwari" to anyone except dogs, or you'll make people angry! ;-)