Im just wondering if this great game can be soloed by one character? Im sure you'd need medical skills at the least, but aside from that, has anyone done it?

It does depend on a lot of things, and it won't be easy, but it is doable.
See here.

If however you mean to play a ninja/stealth/assassin and clear all sectors, then you propably can't mostly due to sheer numbers, aka you'll run out of ammo.

It totally can. That's how I tend to play through actually. Firstly you'll want to try your hand at a bit of stealth. That way you can get your throwing knives out of the enemies after you kill them, thus solving the ammo issue. Ambi-dextrous with a couple of silenced sub-machine guns is good too.

Alternatively you can take the "hide around the corner" tactic. It's not great fun, but once the game's up with all the sneaking, just find a room (ideally with no windows), hide two squares in from the door, then fire a shot with a loud gun. They will dutifully walk one after the other into point blank head shots.

As you get on, you'll find that the old climb on a building, lie down, wait, stand up and shoot, lie down again, is also a necessary tactic.

Now tanks get tricky. You'll need to basically load up with tons of mortars and LAW's then dump them when you actually get into the sector in order to keep your weight down. Possibly then retreat, sleep to get back AP, then go back in again. After that you'll need to just make repeated trips over to your tank buster stash every time you come across one. Make sure that when you attack Meduna, you go for the airport first, so you can be getting more heavy weapons flown in while you're clearing it.

The crepitus were really hard, there ammo is nearly impossible. Basically stack up with as much hollow point as you can, keep moving as they are too tough to go toe to toe with. It took me a while to get through them. Once again you can help yourself a bit by stashing a load of ammo in the second screen of Drassen mine, that at least gives you a couple of screens head start.

This is all for vanilla JA 1.12 btw, I expect 1.13 would be too tough. With all of this, you still need to save very regularly (keep a different save just prior to entering an area, so as not to find yourself completely stuck, then recycle 1 or 2 when you're in the actual combat zone).

With LOAD and SAVE, you don't need Medical at all. It is definitely possible to go through the game without ever taking a hit.