so does that mean D Dorian is composed of this scale? D E F G A B C D

I'd say its in Em with Bb being a secondary dominant. which is a note pulled out of another key and changes the key of the song for that chord.

soloing over with em pentatonic may sound better than G since your chordal riff has an em in it while their is no G chord in it. Em has the same notes...

First off modes do not change the key they only determine what scale step the scale starts on and their are different types :Ionian-1 Dorian-2 Phrigia...