The mouth lock, and the fact that one is not eating, may be related to a dominance display. Often fish who "lock jaws" are "wrestling" and the one may definitely be dominant. If they are established fish, I suppose it might be a mating thing, but I am not specifically sure. In general it is not - but not to say it is not in these guys. How long have you had them?
How old is your tank and what are your water parameters?
How long do you keep your lights on? There is some variation on this...in certain tanks, too long may contribute to algae blooms (often related too to water quality).
I don't recommend feeding brine all that much unless it is soaked in zeo, selcon or similar. It is pretty nutritionally poor. There are a variety of marine flakes, pellets or frozen formulations to feed the fish. The anemone, however, needs something much more meatier like pieces of shrimp, squid, silversides, krill. Use long forceps or a bamboo skewer to get it to the tentacles, and it should close on them. Sometimes it may not, so remove the uneaten food. But brine and flake is really not suitable for the anemone - tends to result in more waste than actually gets to the anemone.
