Yes to both. My laptop has HDMI & TRS out. AFAIK, the soundcard is not capable of emitting to both HDMI & the TRS port simultaneously, but it's also not something I've ever wanted to do, so I'll admit that the limit of my use case there.

(I'll use a bluetooth headphone, if I want audio while pushing something to HDMI. Though I could see using TRS headphones being a nice to have, and I honestly don't know how to configure that, or if it is even possible, since it's all represented as one card in PA.)