Adding stony corals at two weeks is risky even for experienced hobbyists. If you are new to the hobby it’s careless and irresponsible. These are living animals we’re talking about and viewing them as disposable or viewing it as ‘I knew better, so if it doesn’t work out, oh well’ is, frankly, just gross. Even adding soft corals at two weeks for a newer hobbyist is really pushing the envelope. Your parameters don’t really make sense, if your tank is cycled, you shouldn’t have zero nitrates, either the test is wrong or your tank isn’t cycled (a two gallon water change wouldn’t take your nitrates down by much, and live rock alone isn’t going to denitrify your tank). What is your alk/cal? If you’re going to keep stony corals, these are values you need to know. Also, the light you have is not sufficient for LPS, and probably not even soft corals, it has a PAR of less than 50 right under the light. Your hammer and torch (and your zoanthids) require more light, they will not survive long with inadequate lighting (they will basically slowly starve to death). And lastly, your temp is pretty low, I would shoot for 78°.
All that said, I don’t mean to just drag you, I want you to be successful, but there are a lot of problems here. The corals are in your tank, so that’s that, but you need to make sure that your parameters are stable and within range (find out what’s going on with your nitrates and start testing for alk and cal and make sure your alk stays stable - cal you want to be stable too, but it’s less important). You also need adequate lighting, make sure to acclimate your corals to whatever new light you add.
Also, in your first pic, it looks like the flesh between the two polyps is ripped, in an established tank that would likely heal, in a two week old tank it’s trouble. You could do an iodine dip (search the forum for directions if you are unfamiliar), but conversely, moving it could make it rip more, so it may be better to leave it and only dip if you see it getting worse or see tissue loss. I would definitely try to minimize disturbing it and just let it heal.