Crossdomain
If you want to keep separate URLs, setup cross-domain tracking, using this.
- Setup a master profile, with no filters.
- Setup a cross-domain profile, per above.
Generally no, you don’t want different profiles for each of them, as you won’t be able to then measure traffic thru the entire site. Each profile is it’s own discrete view of the data. If you create separate profiles you won’t be able to report off a single, contiguous session on your site.
Also, it’s a good practice to setup your web server to always redirect to the main URL that has the certificate… in your case have MySiteExample.com redirect to www.MySiteExample.com.
Finally, this kind of question is actually better asked here: https://webmasters.stackexchange.com/
EDIT:
To clarify on the http and https, you don’t need to do anything in the property / profile configuration, since they are the same domain. Further, the script that you include for Google Analytics handles avoiding mixed mode (https and http on the page). See this: https://developers.google.com/analytics/devguides/collection/gajs/#quickstart. Specifically, the following javascript line handles delivering the script via https or http, depending on whether the page was retrieved via http or https. In processing, google analytics doesn’t care if you are using https or http.
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';