Is there any builder site for bicycle?
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.