A little later, but just recently i switched a v1 site to use ssl certificate.
No problems encountered EXCEPT already PRE-used 'absolute' url's.
After changing these, everything alright (site was running quite a long time, so time of installation
has no influence). SSl certif. was installed, and use of ssl activated. No more, no less.
Prefs should mention that the base url is using httpS. (my case no redirection used)
So when i do run your mentioned examples. nothing is out of the ordinary, so seeing that, it also
may apply to the theme you are using or specially crafted plugins that do use absolute url (paths).
Hardcoded url's will NOT be automatically become httpS