If you can seperate the two corals they will be much healthier in the long run. The tentacles are refered to as mesenterial filaments. Basically feeding tentacles but also used for defense against encroaching corals. It can use these tentacles to consume/attack nearby animals or capture prey. It's actually quite common to see them out at night, nothing to be concerned about. It's actually the best time to feed them, finely minced raw meaty seafoods or enriched mysis works well.
As far as the algae, do try to pick some off. It will feed off the phosphorus bound up in the coral skelaton and can take some time to eliminate. Use a very fine soft bristled toothbrush and be mindful not to brush the fleshy crown, just the hard skelaton. The algae will get caught in the bristles and should be fairly easy to remove. You can also just pick it off with your fingers if they can get in there.