Menu Database

I have this idea which is basicly a menu database that you go to in the main menu to find out about everything you find in the game, like the history of the T-800, it's valnerable points, and all that stuff. Plus if you want I'll do it, I mean write it all down.

That would be a great understructure for the plot as well as great fanservice. would the one in Arkham Asylum be an example of inspiration?

Yup

It could be a reward for finding collectibles. or even just progressing through the campaign.

or you kill X many T800s, you unlock information about the T800.