Should I indicate on my CV that one of my papers is an invited paper, when I am one of the authors, but not the invited author? If yes, how do I do this? Should I list it with my other conference papers but with a remark, or should I create a separate 'Invited papers' heading?
I believe that the key distinction here is not whether the paper has been "invited" or not (since there are lots of different types of invitations with different implications), but whether the paper has undergone meaningful peer review.
If the paper has undergone a normal peer review process, it doesn't matter whether it was invited or not: it can be reasonably collected with all of your other peer-reviewed manuscripts.
If the paper has not been peer-reviewed, then it should be separated for listing as a non-reviewed publication---still potentially significant, but definitely a different category. Again, the invitation itself is not really the issue, but the standard to which you have been held before publication.
There is no distinction between the "invited author" and the authors who submit the "invited manuscript." All of them are equally eligible to use the "invited" label for the work in question.
The reason for this is that the inviter needs to contact someone to get the process started. Just because you're not the specific individual who was contacted doesn't make your contribution to the invited work any less significant.
As for how the work is designated, I mark such talks and articles as "(Invited)" within the standard sections.