If you back sweetened and primed without a campden tablet (sodium or potassium metabisulfite) then you will need to pasteurize shortly. This may be a day or a week+ depending on factors.
Cider gets better with age but I've had some good "samples" after 60 days total time.
Yeast eat sugar. That's what they do. If you backsweetened with something that contains fermentable sugar, then (under normal circumstances) the yeast will eat it. So, you would have to pasteurize or do something to stop the yeast to prevent overcarbonation and possibly bottle bombs.