1. You will have to pick up your luggage at GRU, pass Customs and then re-check your items to GIG. There the ground staff will be able to assist you in finding possibly another flight GRU/GIG. Or even better, try to get a flight out of Congonhas (CGH) directly to Rio-Santos Dumont (SDU) - be careful that TAM does not charge you any extras for it. There is a bus service by TAM free of charge between GRU and Congonhas.
2. I have not understood what you meant in this query
3. TAM is pretty nasty in re-scheduling your itinenary unless you are a Vermelho card holder in the Fidelidade FFP. Mainly in international flights! Better make sure that you do understand the rules of your fare and re-booking fines.
Hope it helped.