x is private by virtue of being the conveyed by an ECDH key negotiation. No external communication is required.
Do the wallets still need to connect directly, without touching the blockchain? How the receiver would learn the amount then?
(E.g. go build elements alpha, and give me an address from it and I'll send you some coins!).
Do I have to be online at the same time as you?
They're required for outputs only, and technically only when there are multiple outputs. Inputs are already known to be in range by virtue of having been created as outputs.
This is about range proofs but I asked about commitments.