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when I standing by the edge of the playing area my bullets hit the edge and get removed straight away (biggest problem, I would say)

I hadn't noticed that before. It seems smaller bullets aren't affected. I guess it must be an issue once your bullets get bigger? I'll definitely have to fix that.

heart placement is not very random, as we can see

Oh, wow! I didn't realize that about the hearts. I collect them right away so I never realized the spawning was messed up like that.

there is nothing to show how many rounds I have actually played here (which is a shame, as I want to show off that I survived for a ridiculous number of rounds.

I should have made it more clear, but in the bottom-right corner, you can see "Current" and "Best." Current is the current round  you are on and Best keeps track of the furthest round you've reached (it updates after you die or replay). Based on your screenshot, you got at least to round 10.

at this point, I can't actually choose the 'present' between rounds, since my bullets are still moving (slowly), and will kill one before I can make any choice

Ahh, okay. I'll need to despawn all bullets when the presents appear, not just the enemies' bullets.

- the 'your bullets convert enemy bullets' powerup is kind of broken, I think (but some brokenness is ok, as it is fun to break builds in these kinds of games) 

Yeah, this one is definitely OP. I'm kind of torn on it because, on one hand, it's broken, but it's also fun to use because of how broken it is. I think a good compromise would make it a temporary power-up you can get.

Thanks for the detailed feedback! And for the screenshot. I'll try your game soon.