As far as Skype, you can tell them simply that it isn’t required for your gig and therefore it is against the Terms of Service. If they don’t accept that and you risk it, you could lose your account here. Fiverr does make exceptions for Skype but only if they are absolutely necessary for the gig and you have permission.
As far as the picture, I looked at your gig to see what was being filtered out. I didn’t see anything on your gigs that says no pic of any kind but I did read quickly. I can’t really suggest anything on that part but if you don’t want to do it, you can tell them no. If they already ordered, you can offer them a cancellation and refund. Don’t do anything you don’t want to do and make sure for next time it is clearly in your gig description.