Is there any reason for the stripes on a talis? Does the color of the stripes have any significance?
From Rabbi Hershel Schachter's YUTorah lecture on the topic:
The stripes are reminiscent of the techeilet (blue string) that everyone used to wear; depending on the concentration of the dye, you could a color anywhere from light blue to near-black; hence some people have blue stripes, some have black.
I believe there are also kabbalistic meanings behind the stripes (try Rabbi Aryeh Kaplan's A Thread of Light), but the above is the simple explanation.
To answer your first question, apparently the stripes (like in a barcode) contain information if one knows how to read them, like place of origin and manufacturer. See page 2 of this interview, which mentions this fact in passing.
The Minhag Yisroel Torah mentions that we currently use black stripes based on the Rambam's opinion that the colr of T'cheiles is actually closer to black.
The stripes of color are a rememberance for the lost blue techeles string. I heard on a tape from R' Yoshe Ber Soloveitchik that the differences in black/blue really come from a machlokes Rambam and Rashi. The Gemara in Menachos says that Techeilis is " Techeiles Domeh Le'Yam, V'hayam Dome Le'Rakiya" that the blue techeiles string is the color of the sky. Seemingly that would imply a light blue. However, depending on the time one is looking at the sky, the color can be drastically different.
The Rambam learns that it is towards evening, which would mean that the blue would be a very deep dark blue, however dying techniques were not exact and therefore black was used. However, Rashi learns that it's the middle of the day, thus a bright blue used.