How do I know when I'm through cycling?

If you started with uncured LR, I don't think your tank will complete cycling in 3 wks. As others have mentioned, you can't depend on your LFS to tell you when your cycle has completed, from the start of things, like most LFS's (at least in my area) they seem to just be in the business to make a quick $. When your parms are stable for a few weeks (and in my opinion this takes 5-8 weeks for the tanks I've setup over the years), then you should have started adding livestock slowly, like a CUC followed by a small fish. Let the tank adjust to the bio-load for a few wks then add another fish...and so on. I wouldn't add corals until 6-8 wks and your parms are consistently testing OK. As far as the anemone, I would wait until the tank is fully established, preferrably closer to a year and make sure you have good lighting. You will eventually encounter algae problems, almost every new tank goes through this phase, it's normal. As far as cycling with/without lights, I've done both and I would run the lights for a few hrs, you never know what you might have living on your LR that you might want to keep alive. good luck.