On the second one, it will be easier to ID once it properly acclimate and the polyps open up. But based on the picture it looks like a favia to me. The "ridges" look hard to me instead of fleshy so that looks like its part of the bone structure, esp the one on the left. That's clearly a frag cut to the bone and not a polyp. Since these bone structures don't tdont look "separate", it points to favia. Also that outer circular opening, if it were an acan lord, I would expect to see the short stubby feeder tentacle already. It could still be an acan that's just very retracted but like I said, once they open up it will be easier to tell.
For example here's mine. First one is an acan, notice how much the flesh part can expland and display the classic differentiating trait of "separate polyps" vs Favia. Note here the red border is extremely fleshy part of the polyp, probably expanded about 1 inch above the bone
Vs my Favia, note how the bone structure all kinda merge together, the purple border here is fleshy but no where near as much as the acan - probably a 1/4 inch layer. Also the dip on the left is very similar to yours - this is the frag cut.
In term of care - favia require similar conditions as acan lord so where you put it is probably fine. However, favias are more aggressive than acans and can release sweeper tentacles 3 to 4 inches long that can sting other corals. That will be the main reason that we want to confirm its a favia. If it is you probably just want to give it some space from your other corals.
Also, ur current lighting just makes it look brown. Put it under actinic/blue and the fluorescence will give us an idea of the specifc "trade name" from the color. Ie, mine is a "dragon soul" favia due to its green/purple fluorescence.