It is good that when a miner solves the block with a transaction( to self of 12.5(bitcoins)(current value) ) and then it propagate it in the network , then 1. how come everybody in the node knows that current value is 12.5 and blocked solved is it is valid ?? is there any authority which say that now 4 years are over then the value should be half ...??
Because every node in the Bitcoin network can count.
The reward schedule is not based on years, but on number of blocks. The reward is halved every 210000 blocks. See https://en.bitcoin.it/wiki/Controlled_supply. Every full node has all the blocks in the block chain, and thus knows how many blocks are between the current one and the genesis block, so they can easily calculate what the current reward is supposed to be. This is coded into Bitcoin Core and other node and wallet software.
No central authority is needed.