What roles has the TIME information play in the bitcoin header?
the time feature really doesn't play a role in the broadcasting of two simultaneously mined blocks. Those are just handled through broadcasting effect, forking and subsequent blocks mined. Time is started from the moment the miner began hashing to solve the POW. Its used to know how long it took in comparison with recent blocks found for the difficulty re-targeting calculation. It also serves as a record to know when a block was mined.