I would like to know how to handle Skype daily.
My Mac is always ON and the desktop phone handling Skype too.
I heard some friends saying if the Mac Skype app is ON, it'll ring instead of the desktop phone.
So my question is, how to use both of them at the same time, with messages going to Mac and voice calls (both skype and skype number) going to desktop phone only?
You have been misinformed. If you have the Skype client installed on multiple computers and running simultaneously then it will ring on all machines simultaneously (minus a possible ringing delay between devices). I have it running daily on at least 4+ computers and it works in this fashion.
The only time rings are missed is if I just get off a Skype call on my computer/device and the client doesn't reset itself fast enough before a new call comes in. If that is the case, the Skype clients that were not busy, continue to ring and the computer I was just using will only catch future calls. This can happen a lot if you end up playing phone tag.
Be aware that sometimes the ringing won't stop on other devices when you pick up the call because you caught the call very late. If that happens canceling the call (decline or pickup/hang-up) on those other devices will usually solve the problem.