When I did this a couple of years ago, I would videotape questions the students had and then send the video to our partner school. Then, the school would answer the questions and then send us questions to answer. We usually did a few questions every two weeks or so. You can upload videos to dropbox and email the video's link. It's really easy.
We also sent a lot of pictures back and forth (food, clothing, school events). My students loved it because they could use their own phones and take photos of anything they thought would be interesting. I remember the students of our partner school loved seeing pictures of my students dressed up for Halloween and loved seeing pictures of my school since it's very different from theirs.
I videotaped my students saying "Hello, my name is______" in Korean, and the partner school videotaped her students saying "Hello, my name is _____" in English.
There's a lot of different things the kids can do. I'll also send your students a care package of snacks and spices they can taste-test.
The Culture Exchange club would only last from September to February since I would need March-May to prepare for our end of the year testing.
It's really easy to do since the students will focus on one project/topic per week.