I don't think Japanese Anemones give a second flowering, particularly if they have already gone to seed.

I don't know, I don't dead head mine as the seeds are liked by the goldfinches. they flower non stop from late july to the frosts in November. nothing to lose by dead heading and then see if you get more flowers.

Thanks Mg and Sbg for your answers to my question. If as you say Sbg the birds like the seeds I think that is a good enough reason to leave them in situ for them.