Does it mean that x and a are to be communicated privately (off-chain) from sender to recipient of coins? Anything else that is communicated privately?
Also, are commitments required for outputs only or you need to include input commitments as well in your transaction data? If including input commitments, I wonder if it makes sense changing their blinding factors, not just copying them from source outputs.
x is private by virtue of being the conveyed by an ECDH key negotiation. No external communication is required. (E.g. go build elements alpha, and give me an address from it and I'll send you some coins!).
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.