I have USB cable meant for Sony Xperia, the USB cable can be detached. Will using this USB cable to charge other phones like Nexus cause any issue?. I am not using the entire charger, I am just using the USB cable to charge through PC. Will it cause any issue to the battery in long run?
No, this won't cause any issues. I am having the same case as yours (using Xperia L's USB cable with a Nexus 4) and haven't faced any issues with Nexus 4 or the Xperia.
No issue but make sure do not use charger which is not your phone's