Can we modern people understand what people in the Tang Dynasty said? If we don't understand it at all, why do most of the ancient poems they left behind still read in Mandarin? ...

Most of the words should be understandable. But at that time, the capital of the Tang Dynasty was in Chang 'an, which is now Xi 'an, Shaanxi, so it should be based on Shaanxi dialect. It is estimated that there will be some written classical Chinese content, which can be listened to by book review. As for rhyme, Mandarin is very similar to Shaanxi dialect, so most ancient poems are rhymed in Mandarin.