Level mockup with all NES restrictions - 3 colors per 16x16 tile (+black)
Well... not entirely, if this is supposed to be only tiles, you're still using too many colors in some regions. Here are some issues.
The HUD also breaks lots and lots of rules assuming you haven't intended to use sprites there. Like I said in an earlier post, I recommend you post the actual palettes you've chosen with the image so it's easier for everyone to check this stuff. Here are my guesses as to your intended background palettes:
If this is correct, it would mean any time you've used the reddish-purple or pink can't work among other things.
No, you can't do what you posted with the sprite, at least not in the way you posted. You don't get 3 colors+black (or whatever the universal color is) for each sprite. You get 3 colors (and transparent). If you choose black for one of those colors, you only get two others (and transparent).
That sprite is black, gray, purple, and light blue which is 4 colors. You'd need two sprite
palettes and sprite overlaying to do that. It'd work like this (The two teals in the second palette are unused):
But sprite overlays should be used VERY sparingly, because of the eight sprite per scanline limitation.
The way to think about it is that the sprites are a layer drawn above the background. So that they can be drawn on top of the background without obscuring entire 8x8 pixel sections of it, each sprite palette has one color always reserved for transparency leaving the three others.
But sprites and backgrounds do not have to share palettes nor tiles.