Is it normal for a database to have 3600 tables?
Those tables are tables for fields. Whenever you add a field to a content type Drupal creates two tables, one to store the field value and another one to store historical data of that field. 

Deleting those table will break your site. 

This just means that you have a lot of fields. Usually, in drupal 7 it is a watchdog table that contributes to the size of your database unless you want to keep historical log data feel free to clear some data from watchdog table.