Perhaps I'll answer you in reverse order here.
pH, my big system runs a pH that rarely drops below 7.6 because I made the mistake of using shells as 40% of my media and they buffer to about 7.6. I still manage to grow stuff though I would probably have less issues with Iron deficiency if I had a lower pH. You can keep your pH where it works well but you may need to regularly supplement with chelated Iron to make the plants happy and some plants may never thrive in the system while others will do better. (I've never had much success with cucumbers or strawberries in my high pH system and I would not even attempt blueberries.)
Nutrients. We know the N is there is we test for that. I think you would find that if you tested the P, it would be there too. Fish feed and fish poo tend to provide those well enough. Sometimes the potassium needs to be supplemented and this is usually where the seaweed extract comes in. Sea salt sometimes can help with this too. But depending on your fish feed, some people don't even need to supplement that either.
Cycles per hour, well that all depends on how you set things up. Some people will use a pump on a timer and a slow drain back to the fish tank. Others will run the pump constant and let an auto siphon deal with draining. Which you use will depend on the layout of the set up and what you want to tinker with. If you don't have much fall from the grow beds to the pond the siphons might be tricky. It can also depend on the type of pump available for the purpose. If it's a small pump that you want to run continuously, then the siphons are the way to go. If it's a larger pump that you only want to run say 1/4 th of the time, the a timer is probably a better choice. Floating raft would not get a siphons and usually should have a constant small flow plus some aeration but you are right about not all crops being well suited to floating rafts (though you can grow a larger variety in a raft than you might think, it just means you can't go lifting the whole raft out for harvest if you have vines growing up a trellis on one end.) You can grow herbs, vines, flowers and other things in rafts but some root crops won't be well suited to rafts and heavy plants would tend to sink some rafts or even grow too big for the holes/pots. So what method you choose should be based somewhat on what you will be growing and how you want it to look. Gravel beds can be quite ornamental while a raft is going to look a bit sad when plants are tiny or when you have harvested a bunch of it.
I will warn against lumber and liner in termite territory. I've been replacing all my lumber and liner grow beds over the past year. Liner is ok so long as it isn't near wood. Termites chewed right from the wood into my liner and I had leaks. Granted, my lumber wasn't pressure treated but even if it had been, that only slows the termites, doesn't necessarily stop them.
If you can, make the beds deeper, especially for the gravel bed if you do go with a siphon, I really recommend 12 inches deep as a great functional minimum, I know it can be done shallower, I've done it but I now really love extra deep beds (most of my gravel grow beds are now 24 inches deep.)
On the siphon you need to keep it's size in the relative functional range for the pump you are using. If you put in a tiny pump and a large bell siphon, the tiny pump will never kick it in fully and you end up with a constantly flooded bed that just trickles over the top of the siphon.
You probably already know this but it is usually pretty inefficient and bad for the pump to restrict the pump flow, it would be best to bypass excess pump flow back to the pond or somewhere else rather than simply restricting the flow.
As to what timing is best, hard to say. With timers, most people flood for 15 minutes and then leave the pump off for 45 but that can be altered depending on season and situation. Most of my flood and drain beds are getting flooded for 15 minutes and then they get between 30 minutes and an hour and a half to rest depending on what system they are part of.
With a siphon you will be filling again as soon as the siphon finishes so you will of course get more cycles per hour. How long it takes doesn't really matter so long as there is some flood and drain action and the water is moving since that is what aerates the water for the plants and bacteria.