Security via Proof - of - Work
It creates a fork.  There's no way to "sever" an existing branch of the blockchain.  All valid branches remain valid forever, and a node will select whichever one is currently the longest (by total work) as the authoritative ledger.
Right.  If you just redo one block, you've created a branch, but it's not the longest one, so it won't be considered part of the authoritative ledger.
Yes, that's the right analogy.  "Double spending" doesn't duplicate money; rather, it rewrites history so that your payment is considered to have gone to someone else instead (typically back to you).  If someone else thought they had that money, and gave you some goods or services in exchange, then you've effectively stolen it back from them.  You effectively got to spend that money twice, but the blockchain thinks the first one never happened, so the official record only shows one spend.