A pair of H. fuscus can be kept in a 20g tank but be aware you still have to be very diligent in tank husbandry to prevent bacteria colonies from forming.
For best chances of success it is not recommended to have tank mates as they introduce pathogens the seahorses haven't been exposed to previously and many many times, fall victim to.
There is no one method of filtration that you must use and indeed there are many working varieties of filtration out there that work for seahorses.
Chillers are only needed if you can't keep the temperature low enough as pumps/powerheads and lights can heat the water above room temperatures depending on the devices chosen and set up design.
Sometimes only a fan or two may be needed.
A sump can increase the water volume of the system making it more forgiving and thus a safer bet for keeping seahorses, but many keepers don't have one.
As to feeding on mysis, that depends on the breeding source of the pair you get, but true captive bred seahorses would normally eat frozen mysis.
If you haven't already, check out the links on the page I linked to in your other thread as most information needed for beginners can be found in those links.
