Simple answer (because the technical answer requires a discussion of the overtone series, and other stuff I'm too tired to get into right now..)
Pedal Bb is one octave below the Bb in the staff...



An F attachment is a feature on some trombones. It is extra tubing that, when opened with a rotor, converts the instrument to an F instrument instead of Bb. This adds to the low range of the horn as well as allowing different alternate positions.

Yup.

More involved answer:

1) Why the harmonic series:

When you pluck the lowest violin string, it moves back a forth, producing the pitch G. Not only does the entire string vibrate as one though, but each half of the string vibrates twice as fast as the whole and at the same time, producing an additional G an octave above the other G. Not only does each half vibrate, but each third vibrates as well--also at the same time--producing the pitch D a fifth above the higher. So does each fourth and each fifth and so on forever.

2) What the harmonic series:

The harmonic series for the first position of the trombone is Bb, Bb, F, Bb, D, F, Ab, Bb, C, D, E, F, Gb/G, Ab, A, Bb, and so on forever.

3) What pedal tones:

We normally regard the lowest note on the trombone as the second Bb on the harmonic series, but it's possible to produce the first Bb (also called the fundamental) too; it's just difficult. Because we think of these notes as below the normal lowest notes, they're called pedal tones.