Rochas:
Hi,
I am planning on using uno to drive another device. The power source that triggers uno has 0V( as +) and -28V (as -). The plan is to use LM7805 to lower the source voltage to feed uno. I have connected -28V to the ground of LM7805 (and 0V to input of 7805 of course), assuming this connection will generate +5V to drive uno. Now is it fine to link the ground from uno to the ground on LM7805?? Or the ground from uno should be used for the circuit that only includes input to uno and output from uno??
That is really not clear as described, I would want to see a schematic drawing to make sure. However it sounds like you have a real likelihood of applying a negative voltage (relative to common ground) to a positive voltage regulator, which will destroy it very quickly, if not also any loads attached to the output of the regulator including such as an arduino board. So try and supply a drawing if you want any kind of validation of what you wish to do, otherwise beware the magic smoke that lives inside electronic components, if it escapes the device the device will no longer function. 