It's ok and only certain corals NEED to be fed. They are LPS corals....
Uhhhh.... no.
The only corals that NEED to be fed are ones lacking zooxanthellae - which are the photosynthetic algae that live in the coral. Sun Corals are one type of corals like this. While LPS corals (just like SPS corals) are carnivores, they will get quite a bit of their "meat" from the water column without spot feeding. Granted... they will appreciate spot feeding now and then, but depending on your tank and your feeding habits for your fish, you may NEVER need to target feed them. I believe Melosu's tank is a testament to that.
Brine shrimp are not the most nutritious things for your fish, and for that reason I'm guessing they're not the best for corals either. Mysis shrimp would be a better option. Spot feeding LPS corals finely chopped clams, silversides, or other meaty foods when their feeding tentacles are out would be even better.
Easiest way to spot feed coral is using a long feeding tube like this:
Nautilus SeaSquirt, Feeders | Pet Solutions
After the lights are out, and the coral's feeding tentacles are exposed, turn off all the pumps and powerheads and just "baste" a little mysis over the coral. After a couple minutes and the corals have their food tucked safely away, turn back on all the pumps. If you have a cleaner shrimp, you may have to stand guard to shoo it away from stealing the food until the corals have it firmly in their grasp!
LPS corals, as a group, do like to be fed, but it is NOT a requirement.
Regarding Bubble Coral lighting - they really don't care. I've read they're normally found in fairly dim areas of reefs, but they seem to do just fine in our tanks under most types of lighting - except strong MH lighting. I've had them at the bottom and near the top of the tank under PCs, and they didn't seem to care. Only thing they might do is change color on you, as they adapt to the new lighting. But that's true for any coral.