A non-living system would be a machine, such as an electrical system, air conditioning, etc. and a living system would be an animal, person, plant, etc.
Gravitational.....................
Yes. You could do this by adding solvents to break down any cell walls, centrifuge to separate the DNA, if you haven't got much then upscale with PCR, gel electrophoresis could be used to detect the DNA, and Sanger sequencing to find the sequence.
