Thanks in advance for reading .So is there any chance that reverse current is sent back by old speakers,from speakers power adapter (which fell down few times on ground) to motherboard's green audio port and affecting/damaging the system.
There is essentially zero chance of that happening. It is unlikely that sending a line-level audio signal INTO the green output connector will actually "damage" anything. And it is equally unlikely that powered speakers can actually send any audio OUT of the input port.
You could clean the volume control by the usual methods (special aerosol spray for cleaning pots and switches). Or you could replace those old plastic things with some modern speakers that will blow those away.