1. How can they claim that they have share/poverty in my flat and I can't sell it. Can they stop me?
Neither your wife nor her father can stop you from selling the property. She has no rights ion the property since it is registered on your name alone. Their notice is not binding on you nor on the buyer.
2. I do not want to divorce her incase she raised a divorce order. I will die but won't sign. Can they take it forcefully?
Nobody can force you to sign the divorce papers but she can very well file a contested divorce against you which you may challenge in the court.
3. I want to file a reverse case on their advocate who put up the notice in the paper if he can't come up with legal paperwork, Is it possible ? As this notice has really spoiled our family name.
You cannot take any action against her advocate, he cannot be held responsible for this notice. Dont get into troubles by having such ideas.
4. She is earning not sure how much as a Yoga teacher. Can she still claim expenses?
You have to prove her income beyond doubt for repudiating her claim for maintenance.
5. They are not allowing me to meet my kids/speak to them over phone. Do I still have to pay their expenses?
It is your duty to maintain your children however you can stop paying the maintenance amount if they are not allowing you to visit the children, let them approach court where you can present your views.
6. What is the probability that they can claim anything against me/My property/My Salary apart from 21 lakhs?
It depends on the circumstances prevailing and how you defend your interests.
7. What are the claims I can do to meet my kids/speak to them legally
File a child custody case with an application for visitation rights to visit the children as an interim relief.