1. It is not a current feature but perhaps in the succeeding versions. However, it can be implemented through custom coding which is just dependent upon your coding skills or you can avail the services of a coder to do it for you.
2. If you are referring to the search form, you need to have a key word entered in the form for it to function properly. However, you can go to a specific category through the categories menu.
3. Yes, it is done that way for
SEO purposes. Search engine cache search result of your site and will bring searchers to an empty page or an error 404 page if the ad is deleted.
4. It is not yet a current feature and will require some intermediate php coding knowledge to implement.