Interesting game. Looks very nice. Music is also very good.
However, I have a few issues.
I didn't notice the spikes at first on the first stage, maybe make them stick out a bit more. Minor nitpick.
I also didn't see the point of collecting the coins. Maybe add a counter of how many collected per stage.
I'd also remove the bullet randomness. It would get a bit frustrating to constantly have to jump and shoot because your bullets are missing and could very well lead to cheap deaths. Meaning starting the stage over again. Others have mentioned this but adding checkpoints would help this a bit.
The gravity mechanic, while cool. got a bit jarring when I went from having a big jump to a relatively small jump. Maybe start us off with normal then have us experience different kinds of gravity.
There would also be a glitch where I wouldn't be able to jump on the edge of a platform.
Overall, I'd say a good prototype. But not without some flaws.