Here's the available :

So, 8 colours, but 16 if you include the BRIGHT 0 and 1 as shown. 2 colours per 8x8px and those 2 colours have to both BRIGHT or non BRIGHT therefore, you cannot have non BRIGHT yellow and BRIGHT yellow or non BRIGHT dark blue and BRIGHT red, for example. Pretty much as standard, the INK will always be black. The sprites will always pick up the PAPER colour of the background (as can be seen by the Humanoid and Robot at top left).
Yeah, I think the background could be too busy. Here's mock-ups without the floor tile in both yellow and white.

I'd rather have some sort of floor tile, though, but the thing I'll have to watch is that the bullets don't get lost in the background.
The sprites are 16x24 px in size and will have a mask (extending 1px around the sprite) so as the background doesn't show through. I'm considering having levels that venture outside, therefore, I'd have to do a grass tile (which I've got already) and that means the background (PAPER) will be the green.
The floor tile is a repeating 8x8px tile. There is no hardware sprite control on the Spectrum, everything is done by software....and it all has to fit into 48K (well, actually about 42K..or 128K, if we ignore the 48K machine and just plump for the upgraded model).