Fishless Tank Questions

[Aquattro]

I've always fed my LPS mysis. They love it, they eat it, therefore I believe it is required. LPS do posess prey capture mechanisms and mouths, so makes sense they need food.
Eric Borneman will insist you feed them regularly. Once or twice a week, directly into the polyps for the LPS.
I've not seen caps actually grab introduced foods, so you might get away with not feeding for them.
You'll likely have worms and such though, that might be a bit hungry, so a bi-monthly feeding of a couple of bits of food might be ok.