No idea about Pech Merle, but both Font de Gaume and Combarelles are really worth it, very close by and you can only get the tickets queueing en place the same day (impossible to book in advance since 2018) so just go to both!

Most caves have some form of electric light, the Combarelles has a number of portable lights that are hand-held by the guide. Without the light you would not see a thing! The movement of the light is essential for the experience. The only cave I visited without any electricity was Bernifal. But you need someone to know someone to contact the old but friendly ‘peasant historian’ owner. He would probably do a tour for your group of students (exclusively) if it is outside the season.

Yes, but you have to phone the number given on the French website. There is also an email address on the site, but I didn't try it. A friend in Sarlat made the reservations for me by phone at both Combarelles and Font de Gaume.