In the second level, the enemy is invincible... as potential though!

OKay. THere are following flaws:
1) Health can go to negative without consequences
2) Going to lava cause restart level withouyt changing health
3) Not all weapon works
4) Fist does not do any damage
5) No description of game control (how to change weapon)
6) Jumoing rope caused characther stucking in oplace, however repeating using hjelped it move

My advice:
Create simple game trying to avoid bugs.

For a first game this is some pretty neat stuff. However there's one elephant in the room that needs addressing.

There's no tutorial or list of controls that I can see either in the game or the description. I eventually figured out the controls but even so it's a MASSIVE gap in the game design

(For those wondering about the controls: WASD to move (W to wall jump as well) and number keys (1-5) to select weapons. Mouse to aim and click to fire weapon)

Also, one time while playing level 2, I was killing the enemy but when he reached 1HP he suddenly became invincible to hits, and when I jumped over him (god knows why) my character got embedded in the ceiling :/)

Jumping physics could use improvement too. All that aside, I wish you luck!

Pretty good little game. Wish it had more than one sound effect though. Also how do I use the sword and other weapons?

To start it off, it's not a bad game. Really, it's not. It has potential but as it is to be expected from someone without much skill in this field, it has it's issues. I like the wall jumping mechanic, it's quite useful. The game however would definetly benefit from a tutorial since finding out how things work takes some trial and error. If you put some more work into it, polished it, hopefully improved the visuals, it could become a pretty good game. Right now, however, it is a bit forgetable considering it's rather crude visuals, basic mechanics. However, for a first 'test game', you did pretty good.