Question : How much time it takes to approve your application once you’ve submitted the application for approval ?
Answer : It normally takes 2 business days. But some times due to some problems it may be delayed. Also one point to be remember that once you’ve submitted the application and it is not yet approve, don’t send the request again since the new request will override the previous request and it will take more time to process again.
Question : can I use facebook application API key for different sites ?
Answer : No you cannot use same API key in more than one domain. You need to get different API for different site, since while creating application you need to give the domain name for which you are creating the application.
Question : If my application is online and running then can I see that how many users are using my application.
Answer : Yes, it is possible that you can see all the statistics related to your application like no of users online, no of users using your application, daily users, monthly users, etc. All these information you can get from the profile page of the application.
Question : If I have an application in facebook up and running can I invite my friends to join my application?
Answer : Yes, you can invite your friends to join your application. Also your friends can add your application to there profile.