Can an old block be inserted into the blockchain? I've been shown how network time is enforced, but I'm still having trouble understanding how a false old block cannot be inserted into the blockchain with the entire chain remined or how a powerful miner cannot remine the entire chain.

Does difficulty prevent this because it would take so long to remine the entire chain, or is there another way that "old blocks" are forbidden?

How are new blocks distinguished from old blocks or new transactions distinguished from old ones?

If blocks older than 2 hours are rejected, how are old blocks never rejected?
Every block refers to a specific parent, resulting in all blocks together forming a tree structure. Typically it's just a single very long branch, with very occasional short side branches (1 to 2 blocks long).

You cannot "insert" a block into the block chain, as no block refers to it as parent.