when i do a database backup will this back up my hacks?
or do i have to install the hacks all over again when i move to another server?

or is there a better way to back up my hacks?

thanks

To back up the hacks you need to back up both the database AND the actual PHP files themselves.

what about the changed templated, are they included in the database backup?

thanks

Yes, the templates are part of the database. However it's a good idea to download backup copies of your style sets in any case.