@john john Pter Thanks for posting your question in Microsoft Q&A, apologize for any inconvenience caused on this.
Are my steps to Fork a GitHub repo inside Bitbucket valid? or I am doing thing wrongly?
Yes, the steps you are following are correct. you can also refer to this similar Github post on how to fork a GitHub repo in bitbucket.
Now let say the upstream on GitHub do new changes, will those changes get applied directly to our Bitbucket?
No, the updated changes in the original/master repo will not be in reflected into your forked repo you need to update and pull the content as mentioned here in the similar SO thread here.
and hence the Azure web App will get a new deployment? If this is the case, then can we prevent this? so we can test any changes done on the upstream before getting them deployed automatically inside Azure Web app?
Once you have set up Bitbucket as the source control for continuous deployment in App Service, a webhook will be created in Bitbucket to monitor any changes made to the repository. Whenever a commit is made to the repository, webhook will initiate a deployment to app service to make the recent changes available.
If you want to stop this kind of mechanism instead of adding your bitbucket repo in continuous deployment in app service you need to create the bitbucket pipeline of your own by using different triggers in bitbucket and add the steps which are required to build and deploy your application to app service.
Hope this helps, let me know if you have any further questions on this.