Do the speed and Damage of a weapon work while in bear and cat form? Or does just the int/sta or other stats like that count? Will the bear attack with the same speed and dps regardless of the weapon?
I am trying to figure out which weapons to use, right now from lvl 12 to lvl 16 1 Hand Mace offers best speed/damage. I was curious also if my 1 Hand Mace skill goes up while fighting in bear form, or does the stave/1h/2h stats dont move while in this form?
Just curious because this bear is so powerful I think i'll have him do all my soloing :)

Bear and Cat form have their own predetermined damage and speed.

Cat form has a base speed of 1.00
Bear form has a base speed of 2.50

The base damage increases each level up and is also affected by stats, attack power, talents, so forth.

As a druid, weapon stats matter more to us than the weapon itself. Agility and Strength directly affect our damage in forms. There's a whole debate about whether strength or agility give us better returns. I forget if the same holds true for bear form, but in cat form:

1 Strength = 2 attack power
1 Agility = 1 attack power
20 Agility = 1% Crit chance

I don't recall the dodge either. So, I'll let someone with better knowledge of status and conversions to our forms fill you in.

When you're in cat or bear your weapon skill will not go up... I've been level 60 for months, but I still don't have Staves at 300 (and I've used Staves since level 1).

I hope that answers most of your questions. Someone else will probably be better abled to answer your stats question.