You may be having bad time with RNG. The game gave me a brutal welcome as well, almost immediately pitching my lv1 team against two humanoids (maybe robots, I don't quite remember) who were apparently the strongest enemy on that derelict. After I managed to beat them and spend almost all monnies to get the team back on their feet, I was about to quit since by extrapolating that experience I could see that I was only making progress towards my demise.
However, I'm now 10 hours into the game and counting, with one game load due to wipe and several successful retreats from too strong enemies and/or encounters under unfavorable conditions. Keep going and don't hesitate to retreat if you see that you're close to wipe. You will probably get a chance to become stronger either through leveling up on other enemies, finding something better in loot, or getting a piece of equipment with rare properties at the shop.
Regarding the topic question... Medic can unlock a "heal self by 1 point per 3/2/1 turns" pasive ability at lv3. I still have to understand if it works outside of combat too. I'm also wondering if Medic can be used less carefully as damage sink due to that, but in my opinion Leader with Taunt, Deflect, Parry and Counterattack can do a better job. In case you happen to draw the needed cards, that is. Or someone with a Tech tool that gives passive Shield recovery.
It appears that the reason my first encounters were so tough was that the ship I first visited was too high lvl- this is illustrated by an exclamation mark next to the derelict node. It essentially means that enemies are a lot higher lvl than your crew.
If you go to any normal derelict it's actually quite easy. The issue with going to a hard ship is most pronounced at lvl 1, as you don't have enough abilities, synergy or flexibility to offset the higher level encounters. Though at higher levels, it's easily mitigated and mostly a non-issue.
I would not advise anyone to go to the hard ship at lvl 1 as it will just drain your resources. I don;t recall getting any additional xp or better loot there either. In fact I'd say the loot I got from the first hard ship was rather poor- the first encounter against 3 janitor bots returned no loot at all.
Thanks for the info on the Medic class, I have yet to try using one. After lvl 3 I don't see much of a point to a Medic as you rarely take health damage. Prioritizing shield strength and regeneration seems to be the cookie-cutter for any class in this game. My leader doesn't even use mental cards because most of the time it''s better to just lay down fire. The only abilities I'm using are weapon cards and shield regen cards and the game is a cake-walk.