Hi, I would like to know if I can start from an older project that I left abandoned. The project just have basic features like a 2D platformer character and some simple assets,  like a template project or something along the lines.

I thought It would fit in "the majority of the game must be made during the week" rule.

Sounds like you're good! Template projects are fine, just change it enough that it's more an actual game than a template :)