Minipets
Well, for #1, you can use an invisible bag – anything in that bag will not be deposited, so it’s useful for other things as well. You can just organize your bags so that that particular one is full of stuff you’d be carrying already or just put it last.
Personally, I don’t think this is the issue with minipets and why you don’t see them. I think you don’t see them because they’re largely BLTC.
Now, I don’t think there’s anything wrong with them being in the BLTC, but without having some discoverable in world they’re pretty sectioned-off from the rest of the game. Even the ones for achievements don’t really contribute to that. Some could be Karma rewards from hearts or sent to you in the letter for completing the heart. Or some could be just found walking around – in a hidden location, has to be fought, rare spawn. These are the reason that WoW is so successful with pet collecting (I stopped playing WoW and find GW2 to be better over-all, but there are some things I miss – this is one).
Without minis being really integrated into the world there’s nothing to get players “hooked” unless they were already interested in the idea from another game or just want to throw money at RNG mini boxes. Now, I think the BLTC pets and how to get them are FINE, but only having them there isn’t really encouraging interest – because then it’s really largely ONLY a pure vanity item and doesn’t show skill or event participation (though there are some) or anything. If WoW hadn’t gotten me interested in the idea of pet collecting already I don’t know if I would have justified spending money on them.
I think your idea is really great, and I totally support it – I just think there are more problems with minis in general, not just making them easier to use.