1.Stats: Should Hypno get a stat boost, Evolution, Mega Evolution or nothing?
In generation I, Hypno had a Special of 115, which went to its Sp. Def, but its Sp. Attack became the same as its Attack. Hypno also has only 483 BST, which is good for its evolution level, 26, but bad overall.
Theoretically, it would need 40 more BST to reach to its original Sp. Attack. This would give it 195 BST gap from its pre-evo, Drowzee.
In a more modest manner, a +10 BST can be granted, but it would not help Hypno.
An evolution would be great for Hypno, not because the evolution would be good, but it would give it access to Eviolite, making it pretty terrifying. But I do not expect that.
A Mega Evolution would be great, but it would require a great Ability, as all of Hypno's abilities are effectively useless.
2.Should Hypno get more abilities?
Absolutely, but Hypno already has three abilities, so that's not likely for now.
Magic Guard, Synchronize, Magic Bounce, Trace, Prankster would all be fantastic.
Due to its high Attack for a Special user, and its access to Meditate, Pure Power would make sense. Iron Fist would also work, due to punching moves it has. Technician for its weak moves and No Guard for perfect accuracy Hypnosis would also work.
Most obvious choices for Hypno is Bad Dreams, however. Magician would also be thematically fitting.
3. Should Hypno get more moves?
Yes. Hypno has an okay movepool, but it is heavily physical oriented due to older mechanics, which is Hypno's weaker point.
It needs a much wider Special movepool, such as access to Electric and Dark-type moves, and Energy Ball. More Poison moves besides Poison Gas would be great as well.
But since Hypno's forte is support, what it really needs is access to Wish beyond ancient events, and Recover.
It's in-game movepool is also a complete disgrace, consisting entirely of Normal and Psychic moves, making Sableye completely immune to you.
4.What additional typing Hypno can have?
Dark, Ghost and Fighting are the most obvious ones. Normal makes some sense as well.
Fairy, Ground and Poison would also be interesting.