How does a crypto exchange utilise HD wallets in practice?

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I understand that HD wallets are now industry standard. I also understand that “HD” refers to the technology of the wallet itself, hence a HD wallet could be omnibus or individual. This said, I do not understand how this works in practice, and where limitations apply. Specifically:

  1. I understand that an exchange may use omnibus wallets for operational efficiency. E.g. they may conduct internal netting between clients in an omnibus to save the cost of on-chain gas fees. However, if each client has their own child key pair and therefore address within the omnibus, can crypto move within the HD wallet to different child key pairs? If not, how do they conduct internal netting? If so, does this mean one could receive crypto to 1 child key pair, and merge/send from a different address?

  2. Can the master private key move crypto from all the child/grandchild key pairs at once, or does it simply exist as a means through which to derive child/grandchild private keys?

  3. Will an exchange typically produce a new public key and therefore address for each client in an omnibus, or will clients sometimes share the same key pair as well as HD wallet overall?

  4. If child key pair A received 1 BTC, and child key pair 2 received 2 BTC, the HD wallet would contain 3 BTC according to the master public key. This said, if I wanted to send 3 BTC as a single transaction, could I do so? If so, which address would the 3 BTC leave from? (child key pair A, child key pair B, the master public key, or a new public key?)

Thank you in advance, I appreciate there are multiple questions here that may not be well informed.

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