If the HDD that i want to use as time machine full of back-ups, what will happen?

- will it become full and want user's to delete all the files and use it back?
- or i need to use another HDD

Time Machine will start deleting your older backups, to make room for the newer ones... It will warn you before it deletes the older backups, so you also have the option to use a new disk..

The answer to your question could be found here.