I rather have a tutorial part of the game rather than a big "Here are the controls on the very first page", super hard to remember. I kept dying in the very beginning to the right, because I had no clue what I was supposed to do.
The music was okay, a little repetitive though.
The background and foreground felt a bit too close in contrast, which didn't make it obvious I could actually jump into the background, I thought it was a wall.
When I finally figured it all out and jumped down into the "cave" and the oil part, it started coming together for me.
Then I got to the bomb part...and I was like what's going on.
The issue is, in most platformers, you don't want to typically fall down into the unknown, so it's again not obvious that you can do that without dying.
Typically, when you lay down a bomb, you run away ASAP. I was trying to figure out how to get the bomb to explode, finally, I figure out, well, I need to light it... but it instantly blows up in your face, without damaging the player, seems strange, I feel like it could have had a delay, with fuze going down for a few seconds until BOOM!
In the one part where you have to oil the block and move with it across the spike trap... I feel like the character should have moved along with it if it was standing on top of it.
Now, with all that aside, I think you have a great prototype/start for a great game. You should continue with it!