犬かどうか分からない・犬ですかどうか分からない
きっと行くと言っていました・きっと行きますと言っていました
いい大学だと思う・いい大学ですと思う
Can't find a passage in the textbook that mentions and I'm not sure where to look. I feel like I've definitely heard something of the sort before.
Your first example is not a quote but an embedded question. です is never used in an embedded question. For example, you can never say ❌駅がどこにありますか知っていますか or ❌誰ですか分からない.
If you are clearly quoting someone else's statement verbatim (i.e., direct speech), the quote can contain whatever that was actually said, including です or any other keigo. In indirect speech, です/ます is generally not used inside a quote.
The distinction between the two is not always clear in Japanese because subjects are usually omitted, and quotation marks are optional even with direct speech. Still, if you hear です/ます in a quote, you can tell it's a verbatim quote.
Thus, いい大学ですと思う almost always sounds odd because most people don't use polite language when they think something in their mind or when they speak to themself. An extremely elegant character in fiction (e.g., a young innocent princess) may use polite language even in monologues, in which case いい大学ですと思いました could be fine, but this is fairly exceptional.
犬ですかどうか分からない sounds unnatural imo, at least based on my intuition. Correct me if I'm wrong though
Natural sentence:
犬かどうか分りません for the first sentence
いい大学だと思います for the third sentence
but your きっと行くと言っていました is correct