Yes they are the first three things which come to my mind when I think of Hyderabad. Pearl and diamond have been the historical significance of this place for trading of Pearl. You will find very good shops out here where you will find nice Pearl jewelry and diamond jewellery.
And about food to releash your tastebuds, Biryani is one of the most happening dishes out here.
Along with that I also remember to Karachi Biscuits which I used to get for sure when I visited Hyderabad.
It's a neat and clean city.
And it is also a growing IT hub in India with most of the IT companies based out of Hyderabad only.
Also find Ramoji film city which is very famous in Hyderabad. Along with that places to visit I would say can be Birla temple Birla planitorium state museum there is water park The Buddha statue in the middle of the lake is the place to see for sure.
Sultan Bazar for shopping. Begum Bazar 2 is a nice place for shopping.