Sponge filters are another possibility and work well under certain circumstances (e.g., nurseries, hospital tanks, quarantine setups).
Seahorses can certainly be kept very successfully in a simple reverse undergravel setup, as long as you are aware of the limitations of such systems.
Sand is very much okay. A thin layer of live sand, preferably black, is the ideal substrate for a SHOWLR (Seahorse Only With Live Rock) tank, which is type of seahorse setup I prefer.
Yes, please. Although seahorses can certainly be kept successfully without the use of a protein skimmer, I recommend including a good skimmer for best results.
The system I recommend is a SHOWLR tank, which I imagine is something similar to the system you are running on your reef tank.