multiple copies of Skype can only run under separate user accounts, making for some unfortunate but not critical overhead. create another user account on your Mac, either business or personal. then from the other one, open Terminal and do:
$ su - [your other username]
$ /Applications/Skype.app/Contents/MacOS/Skype &
after which you can close the terminal.
edit: after running this after a bit, i should note that you will run into fun issues like separate clipboards, links opening in separate browsers, and possibly other multi-user issues which i havent run into yet.
Sharing apps is actually pretty easy.
On your iDevice, just go to Settings > Store and sign into the account you want to download purchased apps from, and then when you go to install them, it will act like it's going to purchase them again, start to download, and then pop up a dialog saying you've already purchased this app, click OK to download again for Free.
I do this on a weekly basis with 2 other accounts and have been doing it for over a year so I know it works. Even on iOS 5.0.
Just be careful to switch to the right accounts when you make your purchases. Since it does not necessarily say that you have already purchased the app, you could look up the wrong app (a HD universal version instead of the normal version, for instance) and end up purchasing it by mistake.
Finally, note that you could sign into your alternate Store account, then go to App Store > Updates > Purchased and see a list of what's available for download on that account, BUT NOTICE that this will LOCK your device to THAT account's past Purchases for the next 90 days!
See: http://support.apple.com/kb/HT4627
"When you turn on Automatic Downloads or download past purchases on an iOS device or computer, your device or computer will be associated with your Apple ID. Your Apple ID can have up to 10 devices and computers (combined) associated with it. Each computer must also be authorized using the same Apple ID. Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days."
Best Answer
Not possible with the official Skype App.
Running unofficial Skype client is possible, but recently Skype changed the rules and pushed out third parties, running Skype gateways (like Fring).