First of all thank you for purchasing our product. After going through your query I can say that it’s a very detailed query which is really good for us to understand your needs. Anyway there are no such plugin by which you can achieve all the things that you’ve listed above.
By the way our theme has only PayPal option if you want to add more you need to manually customize it & add other payment gateways.
Now our theme has option to set whether you want to publish the ad on posting or keep it pending from theme option. Also there are mailing system by which you can notify user when the ads published or other etc you’ll find option in theme option. Also user can edit/delete their perspective ads from profile which is included also. If you get reported ads there are no option in the backend to identify but it’ll notify you via email that which ad is reported & you’ll be able to edit/delete the ad from the link given in the mail.
For other things you’ve to customize the theme by hiring someone expert who can achieve all of these things for you. You’ll not be able to get anything that you listed by simply a plugin instead you have to customize the theme according to your need. As you have a model website then I think customization would be the perfect choice for what you want.
Hopefully this reply will make you understand about the theme & what you need to do to achieve the list.