777 for the image folder does not sound good. Try, if the images still can be displaed, if you use 750 (might be the case). If so, that is enough.
Security should be fine, if you use one of the latest versions of MediaWiki 1.20.3 or 1.19...5(?) and the newest versions of the extensions, which you might use. I do not understand the question for the folders(?) and files to check. All the files in that folder should either come with MediaWiki (and so be updated when you do an update) or they come from you or your users (images, extensions and custom skins). In the second case you have to take care to update them (custom skins and extensions) as needed.
If you have spam problems, combating spam should help.