(Django) Running asynchronous server task continously in the background
Django on its own doesn't support any background processes - everything is request-response cycle based.
I don't know if what you're trying to do even has a dedicated name. But most certainly - it's possible. But don't tie yourself to Django with this solution.
The way I would accomplish this is I'd run a separate Python process, that would be responsible for keeping the connection to the device and upon request return the required data in some way. 
The only difficulty you'd have is determining how to communicate with that process from Django. Since, like I said, django is request based, that secondary app could expose some data to your Django app - it could do any of the following:

Expose a dead-simple HTTP Rest API
Expose an UNIX socket that would just return data immediatelly after connection
Continuously dump data to some file/database/mmap/queue that Django could read
I want to let a class run on my server, which contains a connected bluetooth socket and continously checks for incoming data, which can then by interpreted. In principle the class structure would look like this:
Interpreter:
-> connect (initializes the class and starts the loop)
-> loop (runs continously in the background)
-> disconnect (stops the loop)
This class should be initiated at some point and then run continously in the background, from time to time a http request would perhaps need data from the attributes of the class, but it should run on its own.
I don't know how to accomplish this and don't want to get a description on how to do it, but would like to know where I should start, like how this kind of process is called.