Filamentous algae - what exactly am I looking at?
It looks indeed like a Spirogyra, or at least a member of the Zygnematales.
And yes, the green things are the chloroplasts (or one long chloroplast?), and they are arranged in spiral.

The "empty" space in the middle is likely the nucleus, and the darker circles within the chloroplast(s) could be the starch accumulated at the periphery of pyrenoids.