A photon's momentum is related to its wavelength, not it's speed. They all have the same speed in a vacuum.
2)
Sure.
> So, a remix of the original question, haha: if we say that a photon has no mass, but at the same time we say that momentum needs mass, then if we say that a photon has momentum we're screwed, no?
We would be screwed, but momentum doesn't need mass.
2) Therefore "momentum" needs only "energy" and velocity instead of "mass" and velocity?
It's hard to put reasons and interpretations behind all this, because in the end we just use formulas and numbers and check them in experiments. It's usually simpler that way.
Be aware that a longer wavelength means a lower energy. Frequency is proportional to energy, which is inversely proportional to wavelength.