Given the size of the larvae, no need for a lot of water, so my small 5L (1 gallon) acrylic tank is largely enough. This tank is full of seawater at 33/34ppm salinity in which I cultivate marine phytoplancton alagae Dunalliela Salina. The light necessary for the phytoplancton is provided by a small 15W fluocompact lamp. Any kind of fluorescent lighting will do, mine is a standard 2700K for domestic use. The light has to be kept on 24/24hrs, or else, for reasons as yet unknown, a significant number of larvae die if you switch it off at night.
I'm pretty sure it's usually sold as artemia food, you could try Liquizel as well as sold by Hobby.
As to the light, some of it could be that it stops the zoes from settling out of the water column, which would be achieved in nature by the greater depth of the water column and the strength of the currents, in addition to the additional food issue.