Depends on the size of the items, for jewellery size items I would stay with investment, for larger, ceramic shell.
Ceramic shell can be done without loads of equipment, but for people who do a lot it makes sense to tool up.
Used some of that special quick setting investment many years ago, 30-40 minutes from wax to metal, so mould was obviously wet and the flask needed a fibre liner to allow for expansion and to allow the steam to escaped without blowing the mould apart, that was gooood stuff!!

1. What are the required items of equipment for ceramic shell? My understanding is that it is relatively expensive to set up. There is a tub with some sort of mixing apparatus and there is a fluidized bed system. I gather that the fluidized bed is for coating the shell between dips with sand. What else?

There is a slurry material that is "supposed " to NOT need constant mixing but if serious about it, use the mixed material (cheaper). I made my mixer with a timer (5 min on 5 min off) and switches to turn off the mixer AND the timer. Cost ???? under $1000.00. Plastic, straight walled barrel, DC, rev. variable speed 1 Hp motor, 5 min timer, 2 switches and waterproof boxes, mixer shaft and prop, and base and tower for motor.

2. Why go to all the trouble of a fluidized bed? seems to me like it wouldn't be that hard to just sprinkle sand on the wet shell manually. Am I missing something here?

Can make one of these for under $100.00. plastic barrel, 3/4" ball valve, tank fitting to put valve into barrel wall. plywood flange to bolt the cut barrel together (air area vs. sand area, piece of thin steel (ss is best but a bit more $$) and piece of canvas and bolts. Mfg'd air beds
cost thousands and this one has worked for 2 decades).

3. what is the difference in burnout procedure?

For a large shell, flash out the wax (few minutes, vitrify - 20 min at 1500 deg F total of about 35-40 minutes. For a large invested piece it could take 5-7 days for burnout and 1-2 days for cool down

there is a fair amount of discussion about how wet plaster investment should be for burnout. From what I gather, most seem to prefer burning out investments wet and hot to get the wax melted out because the mold is more conductive to heat when wet and gets the wax melted before it can expand and crack the investment. Are there issues with steam explosions in this rapid wet heat method?

Not really any problem, very porous material.

Presumably ceramic shell would have less problem with this since it is thin and porous and steam would escape more easily.

Not a problem with either, but shell is very porous...

4. what are the differences, pros, and cons, with steaming wax out of shell vs. plaster investments?

To steam either to remove the wax means another piece of expensive equipment. Invested pieces (small) can be put into a hot oven while wet and the wax burnout and the investment is heated to required temp for required time for investing. Works fine. Shell is same but the shell has to be heated very fast to get the wax melting on the surface next to the shell before the interior of the wax gets hot, expands and cracks the shell,,,, same with the plaster invested pieces.