What is this plant with pink flowers and maple tree shaped leaves?
It's a Japanese Anemone (Anemone hupehensis); if I had to guess, I'd guess it was the cultivar "Robustissima". 



I used to grow these when I had gardens. Absolutely you can divide them! Wait until the spring if you can; if you have to divide in the fall, wait as long as you can to do so.