How many miners should validate a block before it gets added to the blockchain? Or does every miner add the blocks it receives to its local blockchain?
The miner adds the blocks it receives to its local blockchain (normally).
When a miner receives a new block he will likely check whether that block is valid. No one forces the miner to do that but if he does not check the validity of the new block he takes the risk of mining on an invalid block. If a miner mines on an invalid block he wastes his resources because the network won't accept his block in case he finds one.
After the miner made sure that the new block is valid, he will probably add it to his copy of the blockchain. I write probably because again you cannot know what the miner will do. He might also decide to dismiss the new block even though it is perfectly valid. He would however again risk to waste his resources in this case.