Dual

yes you can appear in the examination in your pre final year of your Integrated course and you will get stipend too, if you qualified GATE and your institution give GATE schoolarship.

Yes there is no doubt about it

The trends of dual courses are not so good nor reputed meanwhile u need to concentrate both on Your B.Tech n MBA so its advised to go gor B.Tech first then MBA .
All d Best !!!!

Yes. Try for gov colleges.

Integrated MBA is BBA+MBA. The advantage here lies in that once you've laid a solid groundwork in you graduation; it becomes much easier to select the specialization of your choice. The five year course gives you a solid grounding in the basics of subjects like HR, Finance, MIS, etc and then hones your skills in a specific area, immensely boosting your job prospects.
Equipped with an MBA, you will have a lot more opportunities in the job market. Since you will have a specialization in a certain field, you will be given preference over someone with a just a Bachelor's degree.