To those learning High Valyrian, (I do not,) when you watch Game of Thrones do you actually understand what they're saying?
Like with any language, it depends on your level and what other sources you've used to study outside of Duolingo. HV obviously has more limited outside sources (as it's a conlang), but there are Youtube videos out there and the Dothraki.org website, for instance, that one could use to supplement their learning.
Generally speaking, when you're still a beginner at a language and developing your listening comprehension and vocabulary, you can only pick up certain words when you listen to people speaking that language. As your skills begin to improve, your level of comprehension improves. Personally speaking, after studying some HV, I can definitely pick out some words and phrases that they're saying in the show, even without the subtitles on (as well as notice some pronunciation mistakes made by the actors occasionally ;P). I was actually very excited while watching Season 8 (at least there was one thing to be excited about!) that I could understand some of the unsubtitled HV in episode 3.
Not that well. In part, it depends on the actor. In the last season, I understood Melisandre reasonably well, but had problems with Daenerys.
But Melisandre's Valyrian is supposed to be more bookish than Daenerȳs's, right?
High Valyrian is High Valyrian. The bits that were in Low Valyrian I didn't understand at all, of course. Emilia Clarke messed up with the pronounciation, I think.
I memorized Daenerys dialogs and when I want to rewatch all those chapters, it is absolutely yes, i do.