When I back up on my exertnal HD drive with time machine can I erase what on my computer HD for more space?
If the data is valuable to you, redundant backups are essential. Time Machine is an excellent vehicle when you have to restore data that no longer exists on your internal HDD.
Mende1's suggestion of using Carbon Copy Cloner is excellent because it gives yous a HDD that is 'ready to go' should your internal HDD fail (as all HDDs eventually will).
For example, I have 5 copies of my iTunes folder, one each on three MBPs, on a HDD devoted strictly to iTunes and Time Machine (this does not include the iPod). One may view this as excessive but since I have over 100 GB in this application, I am very comfortable with this.
I advocate that the best backup strategy is Time machine combined with a boot HDD and a third HDD for the most important user data. If there is non essential data, the you may certainly compromise and use just Time Machine.