Grid-based 2D game (turn based): How should I get started?

Hello,

I'm a student in a technology class, and I need to create a 2D and 3D game for the class. I can easily create the 3D game, but I'm having issues designing the 2D game. I know what I want to make, I just don't know where to start with the design.

1) How should I design my assets? Would I be able to use any normal pixel editor software, or do I need something specific?

2) How can I set up a grid-based movement system in my game?

3) How can I set it up so that the player moves, and then the computer moves?

4) How can I set certain different attributes to different pieces, for example giving some pieces the ability to give extra health/movement speed? I'm sure I won't be able to get into the real complex stuff like designing pieces that can change the field, but I'd like to get at least that down.

5) I want every move made to leave behind a space filled, a bit like a classic snake game; I want that move "tail" to also serve as a sort of health bar (that can be enhanced by other pieces, as described above). Is that a bit too complex for my level of design, or is it easily doable?

6) If you're wondering what exactly I'm describing, it's an old game that I absolutely adore and want to re-make, here's the link: Spybot: The Nightfall Incident

I could really use some help, I've seen and heard some great things from this community, and I can't wait for your responses!