I struggle a bit with topics like this because there's a large difference between "what's possible" and "what games generally did". I have seen some mockups get called out for being "too good for NES" when they weren't, and things people accept that really wouldn't have worked. Going for just the aesthetic without following restrictions to the letter is fine.
If you're really dedicated to the restrictions, you'd have to post specifics for what you have in mind.
..can I make the game using only 16x16 pixel tiles? is that common in NES games? when I look at spritesheets they tend to be ripped out at 16x16, but people have noted many games are 8x8 or 8x16 only. Got me confused, but I think it will be easier to make it in 16x16 blocks.
NES hardware doesn't deal with 16x16 background tiles at all, just 8x8 tiles. Most pixel artists for NES games still "think" in 16x16 because each 16x16 pixel boundary in the background can generally only be one background palette as was mentioned. But a single 16x16 tile will take 4 tiles as was also mentioned. (8x16 tiles is only for sprites, and it's kind of crazy to explain. But it's still really just two contiguous 8x8 tiles in the set.)
...I noticed many NES levels consist of about 10-20 tiles tops, in some cases much less for backgrounds. Why is that? The limitations to me seem like you can use more than that.
It'd probably help to name some games, but this is a more complicated question than you might think. Something to know about the NES is that not all cartridges are not created equal. That is that different games using different cartridges could do and have wildly different things, and have wildly different amounts of space for things. However, each time you wanted more space or more features, it added to your production costs.
Super Mario Bros. had 256 different 8x8 background tiles it could use. It had 256 different 8x8 sprite tiles it could use. It is a game that contains no "help" from its cartridge, so it literally could not have had more than this. The total space for both the background and sprite tiles is 8KB
It would have taken me more time than I was willing to spend to get exact counts of background tiles vs. sprite tiles for Kirby's Adventure. But the game has 256KB of space reserved for both. 32 times what Super Mario Bros. had!
And so... Kirby could afford to dedicate an entire 256 background tile set to a single type of level, while Super Mario Bros. had to dedicate just parts of its single 256 tile set to each type of level.
There's a lot of nuances to even this, though. Like... Kirby is using more than 256 tiles in any level where it's animating water or clouds or whatever because it's swapping out part of the set of tiles to get the next frame of the animation. It's not even necessarily correct to say only 256 tiles can be DISPLAYED at once. Kirby's HUD is actually a totally different set than whatever the rest of the level is using, so if the current "scene" is using a bunch of tiles the HUD might push it over 256 and that's fine. The rule here is that the switch to a new set must happen mid screen vertically. The left half of the screen and the right half of the screen could not have 256 tiles from a unique set each, but the bottom half and top half could. (or the top 3/4 and the bottom 1/4 or whatever other combination of this. You could even do multiple swaps across the screen, but that's getting into crazy territory.
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There aren't even really any rules on how many tiles you could get per level. Kirby animates water by swapping out part of the set every few frames during gameplay. But you could also do something like that as you progress through a level. Imagine a level where you start on the beach, walk to the plains, walk into a forest, and walk up a mountain. During the first part of the level, you have the beach and plains set in memory. You can have both beach and plains stuff on screen together. Then, as you travel so no that more beach is visible, you swap the beach set with the forest set. Then you can have both plains and forest stuff on screen at once. Then as the plains pass out of view, you swap the plains set with the mountain set.
There's even one cartridge type that lets you get 16384 unique tiles available at once which is more than you could even fit on the screen. There pretty much aren't games that did this (manufacturing cost), so if you did people would call you out.
This is part of the struggle. I could say, "You're absolutely limited to 256 tiles per level." It makes it easier to explain, but it's a lie. "Most games don't use more than 256 8x8 background tiles for a level type." "Most games don't use more than 256 8x8 sprite tiles for a level type." "Most games only get one background palette per 16x16 pixel art." I assume you want most games quotes, but even then... there's not a lot that applies to most games.
All of this is part of why it's really hard to write an easy guide on restrictions.
I tried here. 
