Does revolutions per second of a baseball...

I'm not a physics professor nor did I stay in a Holiday Inn Express last night. But the more revolutions per minute the ball has the faster it's going.

Generally speaking yes. However, there are environmental factors and angles that come into play due to gravity.

Yes, but it has more to do with the quality and potential of the breaking ball.

The answer depends on which velocity you are referring to and also the context of the question.

In a thrown baseball there are 6 degrees of freedom (three rotational, and three translational). Any rotational velocity component is directly affected by a rotation - in that direction. However as per definition of a degree of freedom, the translational and rotational coordinates are independent of each other, which means that they have no interdependence on each other.

Here is a visual: https://en.wikipedia.org/wiki/Six_degrees_of_freedom

Perform the thought experiment:

A knuckleball with no rotation with v translational velocity.

And a ball with ω rotational velocity and no translational velocity.

This proves independence of d.o.f. (At least until further discussion below).

This being said, this perspective is limited in that this analysis neglects phenomena from fluid mechanics. There are effects, with which every baseball player is familiar with that create a dependence with a change in velocity on the rotational velocity. It should be obvious that for a curveball the greater the rotational velocity, the greater the deviation from the sagitta. (But, a curveball actually curves a lot less than you would think). 

As far as fastballs go, if you want, I could get into Joukowski Lift Theorem which relates rotational and translational quantities, but I'm sure for just a simple internet question this isn't necessary. (The theorem is for cylinders, but it's the idea that's most salient).

Fluid mechanics have such an important effect on the flight of baseball, although it is not really an advantage as a baseball player to know such things as what the drag crisis is, because in the sporting game purview it is insignificant.

To (not) answer your question:

As for everything in physics, the answer is only as good as the model you choose.

Yes. And while horsepower gave a rather detailed response, the simpler reply is that generally more rotation = less drag (as a baseball isn't a perfectly smooth sphere).

Think along the lines of the dimples on a golf ball...