The bust system is custom, so it's an ongoing process to work out all the kinks. Thank you for the report!
>Also, may not be a bug, but while the other new party swap in skills are instantaneous and allowing another action with that character, Carina's Divine Intervention requires her turn to take effect
There are six party swap skills and they each have different parameters. Some are instant, some are not, but their descriptions should state that.
>I admit, I'm not sure how that works. If you grab them before Lustlord's Palace, does Ginasta join with her new abilities?
The new abilities should be gained via leveling, so it should work out either way.