1.6. Is the device damaged, if it is running despite empty reservoir?

No. For the devices with pumps (for e.g., Lubrimat / Sawfix / Toolmat / Centermat / Pulsomat), air can get into the piston pump even if it is completely empty. It has to be deaerated only then (see operating instructions) and the feed tubes possibly have to be refilled. Should this happens often, the installation of a float switch is recommended.