Eggs usually hatch somewhere between 12-20 days after being laid and is quite dependent upon temperature. I wouldn't expect them to hatch before day 12 but it's been known to happen.
Sea Monkeys ARE Brine shrimp so yes you can feed them to your babies but buying the tiny packs of sea monkey eggs can get expensive especially if you have a lot of mouths to feed and you will need freshly hatched monkeys at first and the hatch rate can be pretty poor for the commercially packaged sea monkeys that we get here in Australia.
You should be able to buy jars of Brine shrimp eggs from good aquarium/fish shops and there are many suppliers online as well. Once you have them it's a simple procedure to hatch them on mass and there are heaps of tutorials online for hatching them at home.
My setup consists of a couple of 1.25l soft drink bottles with holes in the lids that I rotate between, marine aquarium salt, a length of air tube and an air pump and the eggs of course.
Fill the bottles with 1L of water and add 1 tablespoon of marine aquarium salt (1 tablespoon of NON iodised table salt with a little bicarbonate soda will give you a similar result). Add 1/4 of a teaspoon (depends on how many babies you're feeding) of BS eggs and give it a good shake. Replace the lid if you haven't already.
Insert the tubing through the lid to the bottom of the bottle and attach the other end to an air pump and turn it all on so that the eggs don't settle on the bottom but are always moving. Place the bottle in a nice bright spot where it will get warm but not hot and you will have BBS in about 24 hours.
I usually do one bottle each day or so as I need them so I have a constant supply.
You can buy special liquid micro food foods in bottles. They are mostly algae and are usually for increasing the dietary value of other foods but they make a great food for BBS, and other filter feeders, and will allow you to keep them alive for several days in their bottles.
I use Nutra-Kol's Nutraplus but there are bound to be others out there. It also helps get around the drop in nutritional value that brine shrimp have after the first 24 hours. You just add a few drops to the bottle each day and they do the rest. It's pretty much the equivalent of the sea monkey food you get but nutritionally better for them and your axie babies.
Good luck.
You can get daphnia and micro worms on trademe, I have daphnia but bought some micro worms just incase and im SO glad i did lol the daphnia ran out pretty quickly even though i'd had it going for a while, i still have adult daphnia in with the baby axys so they are providing some baby daphnia for them to eat but i give them micro worms a few times a day, to make sure they are getting enough food