That may be the case for many people across the "Hindi belt" of northern India. (Hindi and Urdu, at an everyday level, being fairly close to a case of "same spoken language, different scripts".) In the Dravidian-speaking south....not so much.

No. People in the northern region would since it is similar to Hindi. Karnataka, Tamil Nadu and Kerala have their own language respectively which is different from Hindi and they wouldn't.

I am not certain about entire Andra and Telengana. People in Hyderabad speak Urdu.

I think you might be talking about Hindi. That is the most common language.

People with an understanding of Hindi should be able to understand everyday Urdu.

Yes because most Indians can speak Hindi(Urdu is similar to Hindi). Hindi is the second or third language for many non native Hindi speakers.