Indeed, Lund is really an amazing place to be for students :)
Indeed, Switzerland and Sweden are both very beautiful ^^ So you're half Swiss if your grandparents used to live in Switzerland?
Yes, we have many houses in the mountains and lots of them are empty haha (because people use their chalets only for vacation purposes). But mostly, Swiss people are living in very densely populated areas between Geneva-Lausanne and Zürich-Basel-Bern.
My grandparents are actually from Sweden but lived in Switzerland for 10 years approximately. My grandpa was working for IKEA in Switzerland at the time.