The first thing you ask is called 'soft body dynamics', which is not in Carrara for now (it is in Poser since version 5 I think, so I do use it from there sometimes, export as obj and import in Carrara).

The second thing is 'hard body dynamics or physics', that is in Carrara. Look it up in the help files as 'physics'. Does work actually, but you need to know and try to figure it out.