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Most shops will do a night dive when requested. However, they almost always have a "minimum" number of passengers. In my experience that's around 4-6 divers. If they don't get enough passengers then they typically cancel the dive. You'll have much better luck doing one on a Friday or Saturday. Call the shop you like and ask them about doing a night dive on the day you want. You should specifically ask about their cancellation policy in case they don't volunteer the information. Surprises on a vacation can be a bummer so it's best to be informed.
Both of those sites are totally doable in a day since they are right across the street from one another, I personally don't do it both because of cost (they are each $35-40 per diver) but it may be worth it for you to check it off your dive bucket list. If you're out doing one of those sites, Rainbow River is about a half hour south of Blue Grotto/Devil's Den and is a much cheaper drift dive ($5 park entry, $10 to take the boat upstream) - you'll want to be here before noon for the boat. For manatees, you'll probably have better luck snorkeling in Crystal River since they tend to avoid bubbles, but I believe you can also dive Blue Springs with them. They are protected so you can't initiate interaction with them unless they approach you first.
I'd forgotten about blue grotto/devil's den. Both are fun dives to do at least once. I've done them on the same day before. As he said, cost is the main concern with doing them both - but they're different enough sites that I think they're both worth doing.
