1. There is no such rule

2. Depends on your sponsor,  but it is generally difficult to get a NOC, You can appeal to the ministry if you feel you have been treated unfairly.

3. There is often a 2 year ban on you obtaining another work visa, I'm not sure if this again depends on the sponsor.

4 Even if your residency  has been cancelled, you can still get a visitor visa. It is easier if you are from one of the approved 33 countries that can purchase the visa on entering Qatar.