Hello,
Do we know what type of cactus this is? The spikes are quite soft. PS, does the plant look content in this condition? (happy pot excluded )

I am also wondering what should my expectations be in terms of cacti flowering? I don't live in a warm or very sunny place, and they are in indoor pots rather than outside

You might check out Ball Cactus (Parodia magnifica) which your photo makes calls to my mind. Also the description of soft spines matches.

As for the remainder, if it is going to be an indoor plant year round, give it as much sunlight as you can. Most of my cacti like a lot of it. Even those that protest when the harsh sun here gets to be too much when it's hitting them directly like a lot of light. Those tend to get reduced hours in direct sunlight and really bright filtered shade where direct sun is sporadic. I'm not sure how lack of light might effect the bloom cycle.

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.

Thank you both

I can see why one would call this
Parodia magnifica also known as Notocactus magnifica
However, since it has white spines I think it might be
Notocactus scopa
Once it flowers you can tell the difference.
N. scopa has a magenta pistil in a yellow flower
whereas, N. magnifica is an all yellow flower