Is Windmill going to be fine without a gun?

Possible spoilers:

I gave him a machine pistol and he ran off and later in the game he gave me 2000 credits as a "Thank You"

So at most I think that's all you're missing. Personally I had over 30,000 credits by this point and it didn't really matter.

A friend of mine said Windmill died, when didn't give him a weapon.

I did the following:

Instead of giving him a trciked out weapon, reload your quicksave and then go down and buy a gun from a merchant. The one in Alice Pod Gardens has a Combat Rifle as the cheapest weapon (1250 credits vs the 2000 you get from doing it), but that ofc requires you don't have a Combat Rifle already, otherwise dump it and buy it and pick up your tricked out combat file when the combat starts.