Translation:I will close the window.
Close the window. < Also fine, especially as there's no "I" word in there... You'd be able to tell by context who's referring to whom...
That is a command in English. The Japanese sentence is not a command; it's just a present tense verb. "I close the window" or "you close the window" (or some other subject) would be an acceptable translation, but the English sentence does need a subject.
The tips and notes section for this lesson says that しめます is open, not close. Not sure how else to point this out.