Yes to all of those, except the last one I'm not too sure about. I've not used their purchase liquidity feature.

I know for a fact that spending out of phoenix via on chain can reduce your liquidity. But this does not take into account liquidity you purchase.

If you haven't used boltz it is a cool process. You can do it either way: LN to on chain or on chain to LN.

In your case it let's your transfer out of your phoenix wallet on the lightning network but then use the boltz exchange to make the transaction end up on chain.

Bolt charges a fee which is similar to the fee phoenix charges for liquidity. I need to do some figuring if the boltz method saves you anything on fees. I mostly like it because it makes it clear in my mind what is going on.