Absolutely, momentum would only really apply in a perfect elastic reaction - whereby the momentum of the player is transferred to the ball. Considering the player has about 500 kgm/s, that would mean a player would need to throw the ball at about mach 3 for momentum to have any application.

That's quite impressive! I get bored after about 22

Not true, I actually changed my wording so that that would not be the case - "mass would only effect the required force to get it to that speed and in that direction".

Just because I didn't make clear what was applying the force doesn't change the fact I didn't exclude air resistance.

Can you work out the path of the ball then (other forces acting on it like air resistance and gravity) using trigonometry then?

i.e. If a static player passes a ball backwards at a 45degree angle at 10m/s, then using trigonometry it's velocity in a directly backwards direction is 7m/s.

If then a second player makes the exact same pass but is running forwards at 10m/s, then it would travel forward at 3m/s? (10m/s forwards - 7m/s backwards = 3m/s forwards).

Using Newtonian physics you can, yes.

To your example, then yes, the ball would travel forward at approximately 3m/s. At such slow speeds air resistance wouldn't have too much of an effect anyway.