We'd met in Copenhagen during our exchange, and we've seen each other about three times a year ever since, even after returning to Japan. We'd met in Copenhagen during our exchange, and we've seen each other about three times a year ever since, even after returning to Japan.

Your sentence is very good, I am just adding a bit of clarification to make it sound more natural.

We'd originally met in Copenhagen during our exchange, and we've seen each other about three times a year since then, even after returning to Japan. We originally met in Copenhagen during our exchange and we've seen each other about three times a year since then, even after returning to Japan.

I really appreciate that we have keptstayed / been in touch for almost four years. I really appreciate that we have stayed / been in touch for almost four years.

kept sounds too stiff

The other one was trying to find hersome new hobbies. The other one was trying to find some new hobbies.

The other one was trying to find her new hobbies. The other one was trying to find new hobbies.

During university days, she often rode a bike, but she hasn't done it recently because of her busyness schedule. During university, she often rode a bike, but she hasn't done it recently because of her busy schedule.

During her university days, she often rode awent bikeing, but she hasn't done itso recently because of hershe has been busyness. During her university days, she often went biking, but she hasn't done so recently because she has been busy.

“Went biking” is more natural in this sentence.

During university days, she often rode a bike, but she hasn't done it recently because of her busyness.due to being busy During university days, she often rode a bike, but she hasn't done it recently due to being busy

"due to being busy" is a little more natural phrasing for this.

During her university days, she often rode a bike, but she hasn't done it recently because of hershe's been busyness. During her university days, she often rode a bike, but she hasn't done it recently because she's been busy.

busyness sounds unnatural.

During university days, she often rode a bike, but she hasn't done it recently because of her busyness. During university days, she often rode a bike, but she hasn't done it recently because of her busyness.

"Busyness" is correct and good job getting that because some English speakers get that wrong! I don't often hear "busyness" used though, so a more natural way to say it could be "because of how busy she has been".

In my casAs for me, I guess it might be good for my health to start playing a new sport. As for me, I guess it might be good for my health to start playing a new sport.

“As for me” is more commonly used and natural, but what you had was also correct.

I'm looking for a gym, but I've no haven’t found a favoritegood one yet. I'm looking for a gym, but I haven’t found a good one yet.

I'm looking for a gym, but I've not found a favorite onone i like yet. I'm looking for a gym, but I've not found one i like yet.