Lvl 3 citys and 4 tiles to built?

And I just noticed that it doesn't tell me I'm missing tiles, like for some other cities (red number besides tiles). Everything is just grayed instead.

Some improvements cannot be built in level 3 cities. Some require level 4 or 5 to build them. Double check to be sure you are not trying to build a building that requires a higher level city. Then double check the required resources (gold, resources, food, etc). Then double check the heirgamenon entry for the city to make sure it says it has enough free tiles left.

Also, keep in mind that there is a bug in city building where sometimes you can build a building twice that you are only supposed to be able build one of. You may have built more of those buildings than you were supposed to be allowed to build because you didn't realize you were only allowed to build one of them. They might be taking up extra tiles on you.

I actually have a couple of lvl 4 cities that have tiles left, however I can't build more, who knows why. My capital ironically has -18 tiles left

and happily lets me build new things,

Each city is alloted 50 tiles to work with. When you build a resource into a city (ie gold mines, farms) so that they are "protected" by the city (Ie can't be destroyed by monsters without taking the city) they use part of your 50 tiles. Now being 4 tiles each resources integrated into the city can eat a lot of space up if you have many of them nearby. On way around this is to plan city placement and building direction accordingly. After all the game doesn't care if your 50 tile city is in a straight line, zig zag or whatever, so its fairly easy to keep from using TOO many resource tiles as part of your 50. I tend to only let one or two very important tiles become part of certain cities.

38 open tiles, and I can't even built a shanty. All buildings are city lvl 2 or less, and the ones I already have don't show up in the list. 

every level city has a certain limit to squares of improvement. Just demolish buildings that aren't houses, and build enough to reach the next level, and you will be able to build the improvements you had before, and then some.

Or at least, that's how I understand it.

I would be so nice if anyone could write like a guide to city building since Stardock was so nice as to forego providing decent documentation.

We honestly need a FAQ for starters. I'll be willing to contribute to it.

THEN we can think about writing game guide.

If you are sure that you have open tiles left, check whether you have enough food to build a shanty. You can only build them with food that you receive from fertile land etc. Generally speaking, it is always a better idea to build enough shanties in one city so it can reach the next level and receives more open tiles instead of building shanties evenly in all the cities you have and all of them are stuck in their level, especially if you are short on food producing tiles. 

Good idea. I'll go start a thread.