Yes, I pictured these challenge dungeons only being accessible one at a time through that Daily Challenge category. All the normal dungeons would still be available in the Dungeon category and through Expert and Level 80 Dungeon Roulettes.
It would probably be best to allow both premades and matchmaking. Many players like to do content with friends and statics but a lot of content in the game is already designed with that assumption in mind. Take PotD and HoH for example. I'd enjoy having a new thing to do with random people which doesn't require commitment.
I think the nature of dungeons being a collection of short encounters with relatively few mechanics allows them to both be challenging and able to be completed in random groups. Coordination via voice chat isn't as necessary if the difficulty comes primarily from playing your role optimally and not from moving to positions in perfect harmony.
This is the hardest thing to plan. It's not good if this new content invalidates existing content, but it also has to be worth doing for some people. I would welcome more suggestions regarding the incentives for doing these dungeons.
This what I had in mind in the opening post. Collectors would like the cosmetic armor from the achievement and also the guaranteed minion, mount and music drops, although they'd still have to win the roll to get those items. I would personally prefer to farm any unique glamour sets with steady progress through achievements instead of drops within the dungeons. The rare dyes could make some money or just be useful for glamour enthusiasts.
The gear drops could be a way of gearing up alts and catching up since there would be no lockouts. Having 5 materia slots would make the gear useful in later challenge dungeon runs (assuming the ilvl sync allows you to benefit from melds) and make the gear more desirable than regular dungeon gear. The appearance and base item level of the gear could be identical to the most recent dungeon gear to save development time (ilvl 375 at this moment). That said, if challenge dungeons were tuned to be very difficult then the gear could probably be 5 or 10 item levels higher.