ok, here goes:
1. Will that tank be good for the seahorses?
yep
2. How many should I start off with? If they have babies, I'm sure it will start to be come overcrowded or not enough food would be available?
if you go to florida collector, he sells 5 gallon setups for 50 bucks. I wouldn't mind getting the dwarves wild caught, but thats just me
http://floridacollector.com/hitchingpost.htm just tell him to leave out any jellyfish (sometimes his thinking is wrong, but hes really good at what he does) OR use that as a basis for what you get. In a 5 gallon, don't be worried if thier population goes into the 20's. You'll see when they get there!!!
3. How dirty will the tank become? Will it be a pain to maintain? On my main reef tank I usually spend about 30 minutes a day making sure everything is ok (regluing knocked over frags, feeding, cleaning off any saltcreep, etc, so I don't mind spending some time on the tank).
VERY. seahorses are dirty fish. think in terms of goldfish. make use of lots of macro algae-in the tank, since the seahorses will LOVE to hitch in it, and live in it. its actually a good idea to have macros in the main display. Since they make the nutrients go bye-bye...
4. Is it possible to hatch the brine right inside the tank?
nope-too much ammonia. Have to make a hatchery, hatch em out every day. there are lots and lots of places that have pictures and diagrams for this. its mostly just a bubbler, and a couple of 2 liters, coffee filters, and bleach. I can send ya to sites that discribe this process.
5. I have three pieces of live rock, is that ok? I will be putting some coral in the tank (softies) that hopefully will allow the seahorse to grab on. I'll add the seahorse last to the tank after it's established.
for dwarf seahorses, live rock is not a good thing-and hitchhikers will probably kill them, and most corals will kill them. They are TINY!
6. My temperatures right now are very steady at 78 degrees, is this too high for them? I may add some fans =/
I dunno bout dwarf seahorses and temps, but with the normal large seahorses, that temp is too high. I'd probably want it around 75 for a daily high, with 72 normal... but I COULD be wrong.
a good rule of thumb is 3-5 x turnover for the water flow. VERY low-most people only use a HOB filter for flow in dwarf tanks, and thats it. a ton different from a reef tank, where more flow is better. In other words, your gonna have ta turn it down.
but NO, dwarves should NOT be kept with other things... MAYBE you can have some dwarf pipefish in there (which are hard to find.)
the tankmates list is for big horsies, not the dwarves.
http://forum.seahorse.org/ they have resources in a FORUM just FOR DWARVES and they can help ya more than most people here can!!! don't get discouraged!