A new block is added to blockchain if more than 50% of miners say that it is solved correctly. Does it mean that all other miners also do the same proof of work by including the same transactions as in the broadcasted block, and same nounce, as used by the miner of latest block?
Each full-node checks the validity of blocks. Checking the validity of a block is indeed done by repeating all steps of building that block and checking for adherence to all consensus rules. If a block infringes any rule, a full-node will consider the block invalid, ignore the block, and ban the node that sent it to him from his peers for 24h for sending invalid information.
As each miner should be running a full-node to stay abreast of the current blockchain-tip, either all miners or no miners should consider a block valid (as long as they are in agreement on the consensus rules that apply).