When you use a hosted wallet run by Bob, Bob is being your "Uncle Jim" and yes, you're trusting him completely with anything that's in that wallet. There are many variants of hosted wallets, but with the classical lndhub style everything is under Bob's control.

Bob is keeping a separate ledger of balances in the wallets he is hosting, and hopefully these add up less than or equal to his actual lightning node balance. Transfers between wallets hosted by Bob arent happening on the lightning network, they are just ledger adjustments between wallets. If one of the hosted wallets sends or receives over the lightning network, well then bob hopefully has enough channel funds and routing to allow it.

You cant use any sats onchain as long as they're tied up in a channel in either self hosted or uncle jim hosted cases. In the case of the uncle Jim hosted wallet, no you cant manage channels and put lightning funds back into your onchain wallet. If you want to do that, you either need to loop them out using a loop service, or you sell your lightning sats for onchain sats with someone that will do that for you (for a fee).