I recently bought Oblivion and was surprised when I saw TES Arena and TES daggerfall on my library. Is this normal? the game gives the other as prizes ? I really don't know but now I want to keep them.

That's normal; buying any Bethesda game on this site (this even includes Fallout 1 and 2, provided they were bought after Bethesda appearing on the site) will give you those two games for free.

Also, don't forget to check out the extras; you'll find Arena's Codex Scientia there, for example.