Hi and welcome to the forums!
Everything you want should be possible, depending on what software you use. I have no experience with video recording software but I imagine any decent piece of software allows you to select which audio source to use for the recording, in which case your CI should be recognized and available.
Using the SM58 for Skype should be as simple as going into your Skype settings and selecting the right input on the CI as audio input. (go to tools → options → audio settings and select the CI input you connected your mic to.)
If the CI does not show then something went wrong with installing the drivers for it.
(assuming you are on windows 7): type ‘sound’ in the start menu and after a short while you’ll see the option sound appear. Click that and see if the CI is listed in both input and output tabs. If not, uninstall the drivers, download the latest version from the Steinberg website and try installing it again.
Good luck with your new toys 
. I’ll be on holiday for a week so if you get stuck I hope someone else can help you along!