Mine is very mobile and goes where he wants. I placed it where I wanted and he up and moved. So after I let it settle where it wanted I had to move corals around and now we are all happy.
IME, once a carpet is happy and settled, so long as water parameters are kept in check and other environmental factors are constant (such as keeping the same lighting), then they rarely move. My gig was in the same place for over a year (then sold it) and my current gig is in the same spot for over 9 months.
its fairly new, so this questions is a "further down the line" kind of thing....
70 gal oceanic tech tank
Tank size isn't as important as tank dimensions. For example, a 60 gallon cube is really nice for nems because it can be placed in the center of the tank. Some anemones --particularly magnifica -- are climbers and if they can feel the tank wall, they'll most likely try to climb up it. Since haddoni like sandbeds, I don't see this happening quite as much.
In terms of your lighting, so long as you keep your bulbs maintained, swapping them out when needed, it should be fine. However, if you notice the nem getting lighter or bleaching, then it's time to consider augmenting your lighting. LEDs work well with carpets.
I too have this question.
Also my understanding is that the Haddoni carpet anemones like the sand, but other varieties may climb rocks.
In terms of carpets, that is correct. You may see both mertensii and gigantea at the base of rocks where it meets the sandbed, but they like to have their foot firmly planted on a rock.
-----
I typically recommend first time anemone owners purchase a BTA to start. They're cheap, hardy, and easy to come by. Once you have experience and develop a comfort and confidence in owning a BTA, you can then move onto harder to keep species -- such as all of the carpets. Keep in mind that many healthy carpets are hardy as well, the difficulty is finding a healthy one. Once you're ready to buy a carpet, research the signs of a sick carpet. Your best bet to find an established one from a fellow reefer.