Here are the answers to your questions:
1. Most travel agents do not deal in Umrah Visas. Hajj & Umrah agents do. However you can try Cozmo Travel telephone number 44073444 and they may help you in getting the visa.
2. The Umrah visa allows you to travel to just Makkah and Medina. If SAPTCO takes you from here to Riyadh and on another bus to Makkah then it is a different story. You will need to check with SAPTCO and their number is 44411322. If they do take you to Makkah via Riyadh make sure you do not move out of the bus station in Riyadh. You may fall into trouble.
3. Yes you need to enter and depart from Jeddah or Medinah if you go by air. If you go by road you cannot enter Riyadh or Jeddah or any other city.
4. Only SAPTCO can advise you on this but even if they are taking you to Makkah via Riyadh you will need to buy the ticket all the way to Makkah from here.
5. No, you will not be allowed to take a flight from Riyadh to India. You can only exit from Jeddah or Medinah.