Is there a way to multiclass companions?

Yes, but you need this mod: https://neverwintervault.org/project/nwn2/other/gui/companion-multiclass-121.

Thanks, any ides how to install this?

Copy the .xml files into "Documents\Neverwinter Nights 2\override" folder.

I never stored my items in a chest, so I didin't even know that there's a problem with this. I have no idea if there's a mod that fixes this bug. Maybe you'll get a storage container in your own keep?

I don't know anything about the "missing chest" in the "tavern room", but if you're talking about the Sunken Flagon, the only containers in it are the benches in the back, and I use them to store my items, and the only time when items vanished from them was at the end of Act 1, when you-know-what attacked and kidnapped you-know-who. The issue resolves, though, as soon as we enter Act 2, the items returning into the benches. I'm guessing that the tavern during the ambush is registered as a different zone, thus the benches don't have any items on them because these are new benches, benches I never stored my items in.

If it wouldn't be immersion-breaking, you could always add a container or two to your inventory with the console.