Is protesting a fundamental right?

Yes, protesting comes under Article 19(1)(a)- Freedom of speech and expression and 19(1)(b)-Freedom to assemble peacefully and without arms. It allows people to question and object to acts of the government by demonstrations, agitations and public meetings, to launch sustained protest movements. The right to assemble peacefully and without arms may be restricted in the interests of the sovereignty and integrity of India or public order.

Further Reading:

• Fundamental Rights – Articles 12-35
• Right to Freedom (Articles 19 – 22)