I like all these suggestions. Not sure if it's implemented in game but 5e allows familiars to cast their master's spells that have a range of 'touch'. So that by conjuring a servant you can basically increase the range of touch spells without risking melee attacks on you character. I think it would be cool if mage hand did the same thing, even though that's not in the 5e ruleset.
I forgot about that and I haven't noticed it in BG3, having familiars regain that would be very awesome and would make them feel so much more useful. It would even help justify a cleric using a feat to get it so that they can cast cure wounds at a range. And giving mage hand that capacity could be cool but as a cantrip it might be unlikely.