So I already have FB app and Instagram application on instagram.com. Now I want to move my instagram application under my FB application is there any option to do that?
If not, my fb app is in live mode and if I create instagram app under FB app it needs to be reviewed and for that app has to be turned to development mode which I can not do as my mobile app is in production and we have users. What should I do in this matter?
There is no way to move the app. You will need to create a new Instagram app, and also a test Facebook and Instagram app. You can then submit the live app for review, but in the submission you can select the test app to be used.