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 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.
Rashi 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, Rambam learns that it's the middle of the day, thus a bright blue used.
R. Dr. Zvi Ron answers that the stripes emerged in the Greco-Roman context (Stripes, Hats, and Fashion, pp. 314-315):
In ancient Rome, there were different toga designs “to indicate precisely the status or the nature of the wearer.” The normal toga/tunic of the average male citizen was called pura (indicating clean, clear) to describe its natural off-white color. The senatorial class had their togas decorated with broad (about three-inch wide) vertical purple stripes,the latus clivus. Members of the equestrian class were permitted to have narrow stripes (about one inch wide) on their togas, angustus clavus. The stripes ran down either side of the garment, close to the edge, but not touching the edge itself. A purple stripe on a garment was con-sidered a symbol of special status. Other groups of men wore tunics with clavi (stripes) of various widths. Material evidence from archeological ﬁndings indicates that the Jews in the Roman era “did not have any distinctive national costume,”however “the customary dress of tunic and mantle (tallit) was altered to conform with Jewish law,” the rules of shaatnez and tzitzit in particular.
While Jewish garments did not appear radically different from others at the time, these changes could make them identifiable as Jews. Because of this, it seems that “the fact that the tallit is striped is probably because of the tradition of clavi bands.” In the 1960s, Yigal Yadin discovered such striped tallitot dating from the Bar-Kochva period. “The remains of tunics found together with the bones of Bar Kochba’s companions. . . are the most ancient garments which are known to have been worn by Jews,” and were found to have “long horizontal stripes over the whole fabric. . . this is still the Jewish tallit today.”
These stripes are also seen on tunics in the artwork of the Dura-Europos synagogue (Syria, mid-third century CE). “Moses’ garment is decorated with dark horizontal stripes which make its decoration identical to that of the second-century remains. One cannot insist too strongly on the importance of what may seem to be only a minor detail of representation: Jewish art and the archeology of Eretz Israel thus combine to produce a single image of the Jewish costume in the period of the Mishnah.” These ancient purple lines persisted as the blue or black lines on tallitot to this day.
Black and white fire, like a Tora scroll has a white background, That represents a clean slate, purity, innocence, the black lines are like the letters representing the information, or the collective individual people that create a group presumably for a narrative towards higher purpose, in fulfilling the tora, justice... Just as the tora has all 613 mitzsvot so to the talit, hope you see the resemblance. though in all reality there's not need to have black lines on a talit at all, it's all minhagim, mine is all white. Now I know this is not going to answer anything from your post though i'll consider it an extra. It's highly recommended to wear wool tallit as per the proper way of fulfilling the mitzvah, and of course you will have many that will say no that's incorrect... the mitzvah from the torah is with wool, you can wear cotton, silk or anything else you want as long as you don't fall in shatnez and your garment has four corners.
Hope this helps.
I can't find the source, but I recall hearing that part of the idea of having the black stripes instead of blue is that although we want to remember the techeles, we don't want to create the false impression that this is the same blue dye so it is made to look a little different. As an aside I feel like 30-50 years ago, blue striped tallitot were way more common in Orthodox circles and the black stripes were more indicitive of yeshivish culture.