I’ll try to answer your questions as much as I can:
It’s not possible to add custom rules in SonarCloud.
You can choose the rules you want by creating a Quality Profile and associate it to your project(s)
It should be possible to stop the merge of the PR on BitBucket side if you have a premium account, you can see more detail here and here. Please note that we haven’t tested this use case ourselves.
Don’t hesitate to come back to us if you have any other questions,