Yes, the F2 should be kept in the fridge. I don't know if it has an expiry date, but I replace it every year.
I don't know the kelvin, but you don't need strong lights. I use an old plant grow light, some people use strips of led lights, some people just put it on the window sill. About 16-17 hours of light per day
The phyto doesn't really need air, the purpose of the air is to keep the culture moving. If no flow at all, the phyto cells will just drift to the bottom and die. So the air bubbles keep it moving around somewhat. In addition to the air bubbles, you should also shake the culture occasionally.
My suggestion would be to start with a single strain of phyto, nannochlorosis is probably the easiest and most common, don't try to culture mixed strains, it rarely works.