Picture one looks like an anemone. Could be aiptasia, in which case you definitely want it out. But it also kind of looks Like a BTA, hard for me to tell for sure. If it is a BTA and your tank is cycling, it probably wont make it, as they like stability in water. And lots of light. I'm not 100% sure what picture 2 is, but they are in my tank too. I've never bothered to do anything with them and they just kind of pop up and disappear whenever. Never seemed to trouble anything. They also don't generally grow big.
For the sake of the safety of your tank, if you didn't put it in the tank on purpose, you probably don't want it. It will save you lots of future headaches!