So I finished the game and got 1 star and now I wants to go for 2 stars, can I use all the weapons and armor I still have or do I need to start fresh?

You need to start fresh and your teammate too.

The 2 stars award was specially created by me after zorg and GONZO beat the challenge mode side by side. I would be happy to see more people doing the same. Just let me 1 or 2 days and I will add a new chapter in the online guide and I will clearly detail all the rules.

The global idea is simple : start fresh, no cheats, no help from other players except if they follow the same path (challenge mode freshly started).

Does that mean I would have to go a get myself killed before I tried for the second star? So I could start fresh? No fair! I want to keep my highscore and keep my deaths to a minimum! How about if I dumpd all my equipment in the startmap and entered the first map with nothing but the pistol?

Dumping all your equipment is a good idea, but you can't do it in the startmap, because the startmap and the mission's maps don't have the same inventory set.
Another solution is to send me an email with your account name, and I will reset your inventory.

Not sure, but adding a reset teleport for the ID missions might be a good idea...

'just walk on the platform and type -reset in console'

Hum, replace "1 or 2 days" by "1 or 2 weeks"
...
Hum, replace "1 or 2 weeks" by "1 or 2 months"

The "reset inventory button" is already on my todo list.
About the 3 and 4 stars award, my plan was to extend the 1 and 2 star concept, but with 3 and 4 players.
The problem will be to control that none of the 3 or 4 players have played with someone else during the challenge. Manually checking the log files for controlling this will be too complicated.
I think about preventing challenge mode players to play with regular players in the next release.