1) If you intend to transit Saudi or visit Saudi, you will need a Saudi visa. Kanz Travel (44883713) can process the paperwork.  No idea as to the cost

2) Exit permit only from your sponsor

3) If there is a car loan, you may need a guarantee letter from sponsor/Qatari National. If there is no loan, no paperwork. Check with the Qatar Automotive Club on C Ring Road (between Gulf Times and QNB) if you need to clarify details. 

4) After exiting Qatar, at Saudi border post you will have to give your finger prints (if you are transiting, sometimes no fingerprinting), get car/contents checked, get Saudi visa counter-stamped by border police, buy vehicle insurance at counter near exit of border post.

5) About 1km from border post inside Saudi, there is a roundabout with clear instructions for heading to Dammam.

Enjoy!