1. Will a single pedestal leg provide enough support for the 24x24 table top? (The top will be used for regular purposes, eating, laptop, writing, nothing abnormally heavy.
Those legs are pretty stout, one should do it.
2. Are there any drawbacks to the recessed floor mounts, other than dirt getting into them?
Not really, you want the mount to be recessed so you don't have an obstacle on thee floor when the table is removed.
3. Do the legs come out pretty easily or can they stick and be a pain to remove and re-install daily?
They are pretty easy to remove.
4. Do the legs have slots and tabs so they stay in one position? I read where someone was complaining about their table spinning.
Generally not, the table will spin if you want it to. If you push down on the leg so it makes a tight fit, the table is not going to spin on it's own, you would have to push it.