welcome to Lucerne hopefully in 2017
I am writing in because I'm just so passionate about the city #CoversEyes lol.
to answer a few of your question from personal experience as a student,
1.Apartments: rooms in a shared apartment cost min. approx. 500/600 every month (higher for studio apartments) I recommend the site wgzimmer.ch
2.Basic Living costs can start anywhere from 1200Chf or less, depending on your lifestyle.
3.Biking/Walking around: In the middle of the city Luzern you can walk to most places and biking is simply great and cheaper here.
4.Language: Although most people get by with just speaking English, it is advisable to learn the local language (German and Swiss-German) to ease communication with locals and basically not feeling lost at train stations etc. haha!
5. Safety: As Switzerland might be the most safe country in the world,that obviously trickles down to Lucerne
it is definitely safe and only general cautiousness(common-sense) is required.
6. Lucerne is very beautiful and has so many sights to see,when you arrive you'd see for yourself
towards the end of 2016 you can proceed with dealing with logistics and planning,BHMS offers you most of the help you will be needing and you have the forum for everything else you might need to know.