What does the term "Longest chain" mean? What does the term "Longest chain" mean, as there is only one 'right' blockchain exists? How another longer chain would make the 'right' chain invalid?
Bitcoin's block chain system is really two quite separate systems, and they are easily confused. The first one is the block tree and the second is the active chain.

The block tree consists of all valid blocks whose entire ancestry is known, up to the genesis block. The rules for validness include no double spending, valid signatures, no introduction of more currency than allowed, ... These are the network rules, and every full Bitcoin node verifies them.

The active chain is one path from genesis block at the top to some leaf node at the bottom of the block tree. Every such path is a valid choice, but nodes are expected to pick the one with the most "work" in it they know about (where work is loosely defined as the sum of the difficulties). Relativity and technological constraints prevent us from doing instant communication across the globe, so two nodes can not be expected to pick the same chain as the active one. This is no problem: the mining mechanism makes sure that the chance two nodes disagree about blocks in the past decreases exponentially as they are older.

So no, there is not one "right chain", there are many. Nodes choose for themselves, but the system is designed to make sure consensus arises quickly.

The rules in practice are this: when a new block arrives, and it extends the previous active chain, we just append it to the active chain. If not, it depends on whether the branch it extends now has more work than the currently active branch. If not, we store the block and stop. If it does have more work, we do a so called "reorganisation": deactivating blocks from the old branch, and activating blocks from the new branch.