I am aware of the Turkish "I" problem, where uppercasing of "i" is different in Turkish and in English. However, does Turkish commonly embed foreign words (e.g. English names) in Turkish text?
For example let's say someone embeds the text "Microsoft Windows" in otherwise Turkish text and I'd like to uppercase the text. Should the "i"'s in the English words (company and product) be uppercased using English rules or using Turkish rules?
Or would the English word already be such a form that uppercasing/lowercasing of it using Turkish rules would give the expected results for Turkish speakers?
Yes, English words in Turkish text are common in Turkey, especially in technical translations.
Also, it is common to see English words (such as "TİP BOX") spelled using a capital I with a dot on the top (in the Turkish style). (Not sure if my example will display in your browser.) If, for example, the word "Microsoft" is spelled as such in uppercase, it would not attract much attention in the Turkish population.
If the audience is the reader group for a technical document, then such mistakes would go noticed.