Does a new site installation run through hook_updates of every module? I have an existing D7 website for which i write hook_updates whenever i have to make any changes to the schema. Now, i have altered the taxonomy_term_data table using one such update. My question is if I install this website in another Schema(Database) will it automatically make those changes to taxonomy_term_data?
Or, do i need to make those changes again explicitly?
When you install a module, the largest number found in hook_update_N hook will be stored in the system table's schema_version field. It will not run the function. Just stored in the table. 

When you copy a module to a new site, any of the hook_update_N hooks will not be executed for you. However, if you would like to make any change, you can implement hook_install to make the necessary database or any other changes.