a) Shulchan Aruch OC 311:8 writes that unlike other tiltul min hatzad, one may move muktza with the foot even for the benefit of the muktza item itself. Additionally, the Biyur Halacha in the end of OC 266 writes that one may move a wallet full of money with his foot.
b) The Mishna Berura 311 sk 30 writes that tiltul b'gufo means not using ones hand, presumably even the back of the hand.
c) tiltul b'davar achair may only be done for the purpose of a non-muktza item, for example if you need the place where it is located. A spoon or broom would be equal.
A garbage can could be moved with the foot based on a) above.