While not yet officially announced as far as I know, it looks like Chromie and Medivh's Heroes of the Storm abilities are now publicly available, so let's take a look!
Chromie will be a Ranged Assassin, and unsurprisingly, her abilities all have a time theme to them (now that I think of it, they really should have done an Infinite version of her instead of a Fel-corrupted one.)
Chromie's trait is rather simple - you get your new talents one level earlier than everyone else (except the level 1 talent, of course.) This means that you'll get your heroic abilities at level 9, and will generally mean that you're a bit ahead of the curve.
Q: Sand Blast
Sand Blast is a long-range skill shot that only hits enemy heroes (no structures or minions) and has a 1-second wind-up. Obviously you'll need to guess where your enemy is headed to make sure this lands.
W: Dragon's Breath
This also has a 1-second wind-up. You'll target an area and after a second it will be blasted with a bunch of sandy bronze-dragon breath. Unlike Kael'thas' Flame Strike, enemy players will not be able to see where you've targeted this ability, so you can be tricky with it.
E: Time Trap:
You can throw a trap on the ground (it looks like an hourglass) that seems to persist indefinitely (limit one at a time) that is invisible to enemies and will put them in stasis for a couple seconds if they walk over it.
Heroic 1: Slowing Sands
You can place a patch of shifting sand in an area that persists as long as you have the mana to keep paying for it. This will slow any enemies who stray into it, and seems to slow them down by more the longer it's been out.
Heroic 2: Temporal Loop
This is actually pretty much Tracer's Recall ability, but cast on an enemy. You cast it on them and a couple seconds later they get teleported back to where they were when you cast it.
So clearly Chromie's going to be pretty tricky to play. She's definitely built to control and take down heroes, and I suspect that the delays on two of her main abilities is going to mean she'll be quite the challenge to play well. Still, there's a lot of synergy here - Time Trap, Slowing Sands, and Temporal Loop will all make it easier to keep enemies where you want them to be so you can hit them with Sand Blast and Dragon's Breath.
I don't know damage numbers, but I suspect that, given the challenge of landing Q and W, they'll probably deal a pretty high amount.
Medivh is a Ranged Specialist. He has some pretty funky tools that can both help allies and crowd-control enemies.
Trait: Raven Form
Instead of a mount, Medivh can transform into a Raven. In this form, he is totally invulnerable and can also fly over terrain, meaning that Medivh can get anywhere safely and also scout very effectively. Probably also very good for flanking enemies.
Q: Arcane Rift
This skill shot will send out a wave of damage. It has a very short cooldown if you manage to hit an enemy hero, but otherwise has a 7-second one.
W: Force of Will
This is a short-duration invulnerability that you can cast on allies. It doesn't prevent CC, but if you've got a friend who's about to take a big hit from a Pyroblast (or needs a second to escape,) this will prevent them from taking all damage. Not sure if this can be self-cast.
This is a bit like a Warlock's Demonic Portal. You create a portal to a targeted area (I think it needs to be within vision range of you.) The portal persists for a few seconds and allows you and your allies to jump back and forth between the two connected ends of it while it is there.
Heroic 1: Poly Bomb
Cast this on an enemy hero and they will be polymorphed into a flying sheep. However, when the polymorph expires, any other enemy hero standing within range will also be affected by Poly Bomb, meaning that if two enemy heroes are standing together and not moving apart, you could theoretically keep them trading back the polymorph indefinitely. Not sure if this affects multiple targets if there are three or more heroes clustered around each other.
Heroic 2: Ley Line Seal
You send a fairly long-range skill-shot out that will put enemy heroes in stasis for a few seconds as it hits them.
Medivh looks to be a pretty tricky hero like Chromie. There's definitely more of an emphasis on working with the team, which should make his trait particularly invaluable for getting to allies who could use the help. On his own I suspect that Medivh will be far less effective, to the extent that I almost wonder if it might be more accurate to list him as a Support hero.