Not sure about the ID. The cactus is probably near its limit in that size pot, which is kind of a bummer given the smiley face and cuteness involved.
This is about the worst time to make a big change in pot size, at least where you are in the northlands, given the imminent cool and dark months ahead. So maybe enjoy the smiley pot for a few months and wait until spring to take action, but I would find a pot 1.5-2 times as wide as the current one and give the plant more space. Wait until the soil is dry, use soil with good drainage (eg. 50% perlite/pumice/equivalent), wait a week after repotting to water for the first time.
As Donald notes you should provide the most natural light possible. A spot right in front of your sunniest unobstructed southerly facing window would be ideal.
