Killifish are the only fish I love more than bettas!
The tank size heavily depends on the killie species you purchase. Aphyosemion Hera is a great fish for a nano tank, while the Blue gularis might need a 10+!
I have always fed my Killifish high quality flake. Daphnia and blackworms were a once or twice a week treat. On this diet my killies flourished for years.
Killifish are very adaptable to their habitat. A heavily planted tank , with certain species, may result in eggs. A bare tank , while boring, is just as good. Both planted and bare will work for killies.
As to temperment, again depends on the species. Some are like bettas and are very territorial. Others are amazing in a community tank. One great community Killifish is the orange australe! Its beautiful orange colors bring a tropical vibe to my aquariums. I would advise against a Gardneri Killie. The males fight and nip at eachother so I kept these in pairs alone.
With temperture, 75-80F works well for multiple species.
Hopes this helps!