F Dorian and Associated Chords

So I have been playing guitar for a long time, but only recently have begun to seriously dive in to music theory. I have limited knowledge, so little that I am unaware if this is a very simple question and maybe I am just missing the obvious.

I am working out of a guitar fretboard theory book, and they give a chord progression: Fmin7 / Bb7 / Fmin7 / C7

And then they go on to say that you could solo over this with the F Dorian mode. I can not see why Dorian would be chosen. From what little I know, the Dominant 7th is the 5th degree of of the Ionian, or in this case the 4th degree of the Dorian, which makes sense in the case of F Dorian we would see the Bb7 chord. But where does the C7 come from? Shouldn't the 5th degree seventh chord of F Dorian be a Cmin7? The C7 has a natural E while the Cmin7 and F Dorian both share an Eb. I was also under the impression that there was usually only one scale degree that was dominant, i.e. fifth degree of Ionian.

This is pretty common. You will see that you are playing in a lot of minor scales/modes where the V should be a minor chord, like in your example, but it will be a dominant chord, like in your example.

This is derived from the major scale with the same name. So, if we are in the F Dorian mode, you can play a chord from the F major scale. The C7 is the V from the F major scale. You are allowed to borrow that chord in your chord progression, instead of playing the V from F Dorian.

It is usually used because the drop V -I sounds smoother than the Vmin - I.

Generally, you can borrow any chord from the major scale with the same name. Another common example is borrowing the VI. The VI in the major scale is minor,whereas in the minor scale it is major.

So you are playing in C major scale and in one point you can play the Ab major chord, which is borrowed from the C minor scale.

F Dorian comes from the Eb major scale - it's the second mode. So it'll contain F, G, Ab, Bb, C, D, and Eb. So, those notes work well over Fm7 and Bb7, in fact they are the main chords F Dorian would have underneath. The C7 chord would share the C, G and Bb, but as you state, the E would clash with the Eb present in the scale. Often, particularly in Blues, it's used, i.e. Eb (flat 3) over a C or C7 chord. It's usually bent up, slightly or all the way to an E natural, but still sounds sort of o.k. left as is to create a dissonance. Technically it's 'wrong', but it does sound 'good'. The opposite, incidentally, is not so good - playing an E over a Cm chord.

If the piece is based around F, then it needs a C of some sort to turn around back to F. The other mode that sort of fits is F Aeolian. I say sort of, as it fits the Fm, but really needs Bbm instead of Bb7. The same occurs on C7 - Cm fits better. That gives the clash mentioned earlier.

Of course, you are not going to use all of the notes over all of the chords, so just holding, say, a long G note over the C7 chord will sound great anyway - avoid the dissonance altogether, if you wish.

As has been said before, make sure you reference the theory with an instrument - hearing is believing.