Yeah, had a look around and there are indeed two palettes, but the only difference is the transparent color as far as I know. There's still a total of 4 colors only obviously.
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Look at the problem from a different perspective: Part of Nintendo's early success was the limited number of controls in most games and their consistency. Sure, there was the odd game where you'd jump using "up" or run using "A", but ignore those.
If you can, try sticking to original gameplay controls, even considering it's not part of the rules. It might make the game more accessible and easier to pick up. Think about why "Flappy Bird" was such a huge success. I'm pretty sure part of that was due to the minimalistic control scheme.
Just try to avoid creating complicated combinations (not talking about something relatively simple as Castlevania's "up + B") you'd see in a bralwer such as Street Fighter without really needing that complexity.
All jams I followed or participated in so far had fonts as one of the exceptions for the "everything has to be done within the timeframe" section of the rules. It would be ridiculous, especially considering some toolsets or libraries have them built in already and these are allowed to be used as well. So don't worry, just look for one you like and use it (of course following its licensing terms). I don't think anyone here minds. :)
Consider it this way: Probably nobody will appear at your door and kick you in the stomach if you break any rule, even the resolution one. :)
Stick to the given resolution, four colors, and use tiles and sprites rather than anything polygonal/dynamic and you're fine in most people's opinion.
If your game plays well and feels like it could have been on the Game Boy it's fine, even it would have been slow as hell.
If you want, look up "Elite" for the Nintendo Entertainment System. Yes, it's been done and it's in full wireframe 3D even though the NES had no 3D hardware (or software) support and essentially tiles and sprites only.
For most it's just for fun, a learning experience, or some creative way to try something new and share it with others.
If you want to participate, just do it. Don't worry too much about the rules or restrictions. Bend them as you see fit, just try to stick close to them.
Also keep in mind the notes above are mixing up GB/GBC a bit. Originally you only had your 4/3+1 grayscale palette and nothing more. The palette swaps for sprites were introduced with the GBC for obvious reasons.
In theory you can use Inkscape, but practically you'll most likely have more work getting your stuff to look good later, even if it's just due to reducing the number of colors (Inkscape will use aliasing after all).
Draw a simple character or object, export it as a 16x16 pixel image (Gameboy games typically used 8x8 or 16x16 for tiles and sprites) and see how it looks like and how much work it is for you to get it right (i.e. reduce it to 4 colors or 1 transparent + 3 colors while still looking good)
To be a bit more specific, you essentially got one background color (the brightest one) and three darker tones to draw on top. You can't really draw with the background color.
For alpha transparency you can fake alpha by letting your sprites flicker (visible/invisible) between frames, which was rather common back then.
I think one could even add blending between frames to improve the effect, since the original Gameboy had quite some ghosting going on.
So in some way you can have alpha, but you'll have to fake it, if you want to stay authentic.