I'm wondering how I can create a .zip file with images in it. Is there any way to do this?
You can do that by calling addAttachmentData:mimeType:fileName: on the MFMailComposeViewController - if you already have the zip file.
If your question includes creating the zip file, unfortunately that is not possible with a few method calls in iOS. You would need to use a third-party library for this, e. g. objective-zip.