I'd like to do long day hikes where I'd eat lunch at a mountain hut (e.g. Rostock hut near Murren, or the hut atop Faulhorn). Do I need to make reservations or do they operate like normal restaurants?
No reservations needed for lunch. At some you may have a short wait for a place to sit, but sharing tables is common and expected.
Any we have been to operate without reservations. From the website https://www.rotstockhuette.ch/index.php/en/ it seems Rotstockhütte only takes reservations for sleeping.