Thanks for playing! Yeah the coin flip is purely random, it starts a little skewed in the players favor (like 60% chance for heads), then increasing your Luck stat raises the chance even more. I originally wanted a few more random minigames to make RNG a bit more of a factor- but as it stands I think that's the only one that you can't win 100% of the time.
Agree on the slot machine too- for how common of a minigame it is it should probably scale more in how hard it gets towards the end of the game. More options or a time limit would probably help with that.
I've got no idea on the actual limitations of the Game Boy outside of the graphical ones lol. Having the NPCs be background tiles is a pretty clever idea, I'd guess the bottleneck would end up being the amount of dialog you could fit in memory.