Not really. Hinduism as the monolith it is now seen as is a very recent concept. The British saw commonalities between the various traditions and customs and myths across the subcontinent and lumped them together into "Hinduism". This has been further pushed to help create a national identity in the last century.

Secondly, India has multiple ethnicities within it. In the northwest, they're primarily Indo-Aryan ethnicities, in the very north, they're more Asiatic/Sino-Tibetan(look at some pictures of people in Assam and Bodo), in the south you have Dravidians etc, who speak languages completely unrelated to any Indo-European languages.

I think what you're looking for is "nationality". Nationality has to do with political borders versus cultural or genetic heritage. If someone is a Hindu, they are likely from India. Hinduism is also the major religion in Nepal (Nepal is actually the most Hindu country in the world), and significant around Bangladesh and Southeast Asian countries. A fifth of the population of certain West Indies nations like Trinidad and Tobago, and Guyana are Hindu.

The real answer is that "Hinduism" is a very vague concept as is, and it covers several nations and ethnicities. I think the answer you're looking for is that 94% of those who identify as Hindu are Indian. Based on your understanding of Hinduism and India, I can certainly see where you're coming from.

I'm not sure if I'm allowed to answer here since I'm not actually a historian, but I am a Hindu Indian American with some understanding of the religion and culture. The short answer is no, they're different. Additionally, many different ethnic groups are also largely Jewish. Generally, be careful when talking about ethnicity since there are so many ways to categorize and it can lead to some fairly heated conversations. That being said, I'll do my best to answer the question as inoffensively and broadly as possible.

Hinduism is a religion and Hindus are those that practice that religion. There are many versions of Hinduism, much like there are many versions of many major religions, but their commonalities and shared scriptures/religious histories make them all fall under Hinduism.

There are many ethnic groups in India. It's a very diverse subcontinent, and you could easily include people from countries that used to be part of modern India, like Pakistan, Bangladesh, Afghanistan, Nepal, Sri Lanka, and Myanmar (I believe that's the current accepted name). I believe ethnic groups can be defined in many ways, but one of the most common is by language and location, so there's (broadly) Tamilians, Gujurati, Malayali, etc. Within these broad ethnic groups, people practice different religions, so someone could be ethnically Tamilian, but also Muslim or Christian, for example.

Judaism is a religion whose practitioners are Jewish. There also several branches of Judaism but they generally follow the same scripture/religious history. Jewish people also comprise different ethnicities, Ashkenazim and Sephardim being two of the major ones. Therefore, you could safely and accurately say there is no such thing as one broad Jewish ethnicity, but several ethnic groups of people who are also largely Jewish.

I hope I answered your question correctly. If I got anything wrong or was accidentally offensive, please let me know. Was not my intention but this tends to be a sensitive subject for some people.