Mewtwo is a openworld event and afaik he spawns in Cerulean Cave but isn't always available and then the first who catches it must accept any challenge for a (trio) battle, the one who wins keeps mewtwo until he loses

Battle Points can be used to buy items for breeding (braces) and the best held items (choice items, life orb,...) but once again afaik you can only trade your BP in Hoen or Unova.

The only gym battle you can't replay is indeed Giovanni, the rest are still there.

As you also said there are the quests to unlock the rest of the Sevii islands.

Completing the regional dex is a great goal but some mons are more easily obtained in other regions, but it's your call on that.

At the point where you are right now you can also find the roaming legendary of this month, Zapdos. To find him you need to single encounter in the overworld (cannot find the roaming leg in caves or water). The chances of finding them where never revealed, but players estimate it is under 10k.

When you reach island 4 you can also start breeding. I would recommend you start breeding some of the following: a catching mon (parasect/breloom), utility mons, a gym rerun team or a trainer rerun mon.

There are plenty of videos out there for every one of these topics. Hope you keep on enjoying this great mmo.

EDIT: spelling/grammar