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You don't need to sleep. Focus. If that doesn't work... caffeine.
Cafe feeds? umadbro? You'll lose way too much time stopping for food that's too fatty to be digested properly anyway. I don't know what gels you use but train on them whatever you choose. I prefer Torq and use their bars and gels and drink, for that matter, during 24s.
You'll probably stop less if you're unsupported because there's no one there to listen to you whinge.
Why fixed? Don't you have a proper bike (ooh sickburn fixie skidders!) for triathlon? Whatever you choose, it might be worth having some spares - be a shame to lose a good result because of a mechanical you can't fix.
hippy-
Sleep: We'll see, but lack of focus (e.g. not strictly racing) will mean it may be better to have a quick catnap rather than riding slowly for several hours.
Only just started using gels for running and get on with them ok, but no idea about anything longer than a few hours. I'll gel myself up on the Ditchling Devil and see how that goes (pop, splutter, pabloosh probably). It's a first go at the 24 so I'm happy to make a bunch of mistakes and learn, but for this first one I'll stick with what I know generally works for me on long rides (a cafe or petrol station forecourt feed every 6 hours or so and some on bike snacking in between).
Fixed: Because I rode PBP and LEL fixed along with most of my other Audaxes and it's what I associate most with long distance riding. I chickened out on a few with gears (K&SW 600, Elenith first time, Midlander Super Grimpeur). Have a perfectly serviceable Wilier Izoard which I'll be using for the Ironman. Using fixed I'm always in the right/wrong (delete as applicable) gear so I have less to think about.
Lack of spares because I'll be coming up on the train so I won't have a car full of spare wheels/etc. It'll be whatever I can fit in a large rucksack.
Greenbank
Somewhere between the two, but more Audax than race. ~350 miles or so, maybe.
Current thoughts are to keep off-bike time down to below 90 minutes (ideally an hour), no sleep (or maybe a 10 minute catnap), two or three feeds in the cafe and gels the rest of the time.
I'll probably be on fixed, quite minimalist (no spare bike/wheels/etc) and unsupported although there'll be plenty of people I vaguely know around so I can leave stuff with them but I won't be looking for food/bottle handups.