@Edent Your example doesn't clarify the origin of Alice's ActivityPub ID.
Handle domains and host domains can be different, yes. See @canary.
Can an actor and objects owned by that actor reside (as in, have their ActivityPub IDs) on different hosts? AFAIK there is nothing in the AP standard that forbids it, but implementations commonly use origin matching to confirm authority over objects. This is codified e.g. in FEP-c7d3: https://codeberg.org/fediverse/fep/src/branch/main/fep/c7d3/fep-c7d3.md
Will you necessarily run into issues? Dunno!