Here's some criticisms I have for these concepts:

60% faster supercharge rate is fine considering what your supercharge only does for you but you're just letting your team down without damage imparing effects or damage buffs. Also it would encourage medics to just go off on their own to fight instead of heal

I like the speed buffs supercharge effect on the 2nd one as it brings a new buff that medics can use. The overheal being removed on disconnect. It would imo encourage pocketing and also hurt your team since medic's 2nd best thing is overheal. The more offensive supercharges like poison and knockback aren't good on medic because as I said before, it encourages them to go off on their own but also be annoying to fight against when he's usually behind his team (like another certain long range class)

For the last one, I also like it for it's unique way of healing (spraying health) and the no overheal stat makes it so that it's not too oppressive. Agility is also fine too because doctors can use it to either make an escape or regroup faster but the damage increase on your weapons again encourage battle medic and with the acid, you are the 2nd fastest class at base in the game and you usually go in with a teammate which can let a doctor go into for a suicide play into a group of enemies to take a good chunk of them out

Try to keep doctor's specialty helping his team instead of him, it's OK to give him extra movement or weapons that are combat suited so long as it can also be good support and has the right downsides to discourage prolonged battle doctor gameplay

Alright, so the last one was kinda rushed through since I had been staring at the website layout for like an hour by then, so here's a revised version (With your advice taken into account)

So a few things of note: for the really weird looking downsides,

The cooldown is to stop you from just spamming a target with the Overheal potion (We don't want another pre-nerf Wraith)

The faster overheal decay is to keep you from being able to just shoot healing at your feet whenever you're threatened (And you you can't be focussing on 2 teammates on opposite sides of Lakeside, since overhealing projectiles could lead to that)

As for Agility, it's basically the same, meant to be an escape for when you know that you can't survive a fight (Example: your patient is oblivious to an Agent or Marksman and gets dropped), but would also let you simple out-maneuver the enemy

I was considering making Strength for all weapon, but I felt that would step on the toes of the Blood Doctor a little too much, but when it's just for melee, it's still good as a self defense tool, and if you're taging along with an Anniknight, it might be terrifying

I think I've explained enough about the Overheal potion