Is there something wrong with having a weapon that is faster than another weapon, and does the same dps? Do you not get as much damage out of it or something?

Also would it affect an assassins PA? Would a faster weapon cause a lower damage PA even if they both had the same dps?

DPS= Damage Per Second
Slow weapon=more damage a hit
fast weapon=less damage a hit
As far as your effectice dps is same, youl do same damage with both weapons, over time.
Pa on uthgard is about cs*10+2melee attacks, or something like that.
wrong formula, for sure, but still simmilar damageoutput(25 lvls with pa on my infi, so far^^).
So, that means, that your pa-dmg will stay simmilar, but it changes, depending on your weapons quality and speed.

+2 melee attacks? So a faster weapon would actually cause more dmg?

thats a bonus, can be set on every weapon. It depends on your weaponability and your weapondamage. As far as they are same with those 2 weapons, youll do lower dmg with the faster one.
The thing, you want to know, it the item-bonus. Yes, it increases the dmg.