6 weeks is what you should wait to cycle a tank. For anemones, the recommendation is that the tank should be established for at least 6 months, preferably a year before adding them. You want to make sure that your parameters are as stable as possible. That means investing in an ATO if you haven't already, and probably some dosing pumps as well. Another reason people will tell you to wait for 6mo to a year is that it takes time to learn about the hobby, and you also need to form good husbandry habits (keeping up with testing, water changes, etc.).
With that said, it does not mean that you cannot succeed. It just means that you will need to really put your best effort into providing the most suitable environment for your nem.
Now that we've covered all of that, let's get to how the nem looks. An anemone that is constantly deflating and inflating is not a healthy nem in my experience. It can be a sign of infection. You also want to watch the mouth and make sure that it is tightly closed and not gaping open or spilling its guts - tough to tell from the pics you posted. It should also be sticky to the touch, although I don't recommend that you go poking it to check either. Instead, if you drop a small piece of raw shrimp on it, it should catch the shrimp with its tentacles and slowly bring the shrimp to its mouth. You also want to make sure the anemone is not detaching its foot from the rockwork.
In my experience, the deflating and inflating is one of the first signs of trouble. Afterward comes the gaping mouth, then eventually the nem will begin to lose its foothold and eventually detach, which is how they end up getting caught by filters/powerheads/overflows.
Just like fish, I would recommend you QT any nem before putting it into your system. Unfortunately, these animals typically undergo a tremendous amount of stress before they ultimately make it to your tank at home. With nems, I like to QT for observation and go from there. If I witness deflating, open mouth, it won't attach, etc, then I treat it with Cipro. If after a 14 day QT for observation the nem is healthy and eating, OR after treating the nem for 7 days and observing for 7, then you can slowly acclimate it to your display tank. There are loads of threads on R2R about how to QT a nem, I highly recommend checking them out. A simple 10 gallon tank half-filled with water, add a heater, small power head and/or HOB filter would work.
As for what could be impacting YOUR nem, beats me. It could be many things - lighting, flow, infection, damage to the anemone's tissue (on the underside or on the column/foot), or it could have already been sick when you got it. At this point, if you cannot QT it, you want to provide it with stable water parameters and monitor it closely. I would try feeding it a little bit, maybe once or twice a week to see if it will eat.
Thanks!
