How can I tell if my vinyl floor is inlaid or contains asbestos?
In the US at least, asbestos was used during and after the 70's. I can't speak for Germany.

To really know if it contains asbestos or not you'll need to test it. In the US at least you can get a kit for about $10 to collect a sample. Then it's another $40 or $50 for a lab to test your sample.

I'd say it's linoleum based on the fiber backing. See if you can melt it with a burning match - vinyl will melt easily but linoleum won't. Do this with a small sample (don't try to light your floor on fire...) and have a way to put it out.

To find out what to do with it, call whoever takes your trash away. The law regarding trash disposal will vary a huge amount by jurisdiction so it's tough to answer exactly.