What I don't understand is:
-do we need miners to validate and "activate" smart contracts once the conditions are met?
Yes.
Smartcontracts are in the blockchain. If the contract condition is "send 1 eth to address", only when that eth reaches the address, and that block is mined, the smartcontract will be validated.
-does smart contract need to passe through a block to be executed? If yes, what king of process work the best (proff of stake?). If no, can I assume that no particular computer power is needed?
Yes, needs a block, as I said earlier. The best and most secure protocol is still PoW, as all decent coins around are using PoW (btc and ethereum). Ethereum is a blockchain designed specifically to run smartcontracts,and they are using PoW.
-lastly, under what form the information would go through the block chain? Would it be tokens?
No, smartcontracts are not made of tokens. The information goes through scripts. in ethereum the language used to design smartcontracts is called Solidity.