Is there any builder site for bicycle? Say you want to build entirely your own bike, from frame to ring bell. Is there a site that can help you with compatibility among all parts? Or maybe you just want to upgrade your crank set but you don't know what else you must upgrade (BB? Pedals? Front derailleur?) 

I'm thinking something like PC Part Picker or Logical Increments for pc's.
Is there a site that can help you with compatibility among all parts?


Yes

There are sites that will let you pick all of the compatible components for a bicycle.

The following are sites built by people who want to make money selling you a custom bike (these are examples of bike builder apps, not recommendations). 

Fanatic.com has a bike builder feature on their website for mountain bikes for a specific set of brands.

Wrenchscience.com also has a bike builder on their website for a variety of bike types and brands.

You can build a bike on these sites and then use the list of parts to purchase from whomever you like.

For an example of a bike builder that does not appear to be tied to a store.
Bike Config is a 3D app that custom builds a bicycle. It appears to be all mountain bikes with a limited list of parts but they hope to grow.

Searching "build a bicycle online" will deliver these and other options.