there is some strange behaviors with the css classes and ids on the search and booking forms

The ids and classes of the block are changing with a random number, this is very problematic as its breaks the styling.

Some forms only have ids but not a class.

A class should be used to identify the forms as related to the Hotel Booking System
An id should be used to identify the uniqueness of that class

Same for fields.

Comments

Status:Active» Closed (works as designed)

The ids are generated by Drupal's form API, which will generate a unique id (ie no duplicates on the same page).
If you're getting weird behaviour make sure you don't have the search block showing on the search page (ie two versions of the one form).
The page and block search forms have a wrapper element with it's own class for theming purposes.