The word 'ich' is just capitalized at the beginning of a sentence. Otherwise it would be a grammatical mistake. In informal writings such as chat rooms, text messages or facebook grammatical rules are not so important and capital letters are used for stressing something, but that is not only true for German. Emphasizing yourself with a capitalized 'ich' might sound arrogant (depending on the context), but I wonder why you would find that remark in a regular verb tense workbook.

No, the 'du' was never always capitalized. When checking books from the 1950s and 1960s you can see that very clearly. According to the current rule you can us bothe the upper and lower case in letters or when addressing a person, but it is recommended to capitalize it to appear formal. There was as well no such rule in the 19th century (source (see page 17 for details): https://www.academia.edu/13123644/Geschichte_der_Gro%C3%9F-_und_Kleinschreibung_im_Deutschen).

I'm not a native German speaker, but I think this is correct: Yes, capitalize it at the beginning of a sentence. The point is just that, unlike in English, the first person singular pronoun is not capitalized *by default* in German. Actually, it’s rather bizarre that the word “I” is always capitalized in English — it’s unclear exactly why we do that. Maybe it just looks funny for the little letter “i” to be all by itself. Side note: “Sie” (along with all of its declensions) is capitalized when it means “you” (but not when it means “she”). When I was a kid, all the words for “you” were capitalized in German, but they changed that rule a decade or so ago. On those rare occasions when I write German, I still capitalize “Du” — to me, it seems polite :)