In mosques, churches and temples in India, it is obligatory to take off your shoes. It may also be customary to take off your footwear while entering into homes, follow other people's lead in this area.
It is disrespectful to touch or point at people with your feet. If done accidentally, you will find that Indians will make a quick gesture of apology that involves touching the offended person with the right hand, and then moving the hand to the chest and to the eyes. It is a good idea to emulate that.
Books and written material are treated with respect, as they are considered as being concrete/physical forms of the Hindu Goddess of Learning, Saraswati. A book should not be touched with the feet and if it has accidentally touched, the same gesture of apology as is made to people (see above) should be performed.
The same goes with currency, or anything associated with wealth (especially gold). They are treated as being physical representations of the Goddess Lakshmi (of Wealth) in human form, and should not be disrespected.
Avoid winking, whistling, pointing or beckoning with your fingers, and touching someone's ears. All of these are considered rude in Indian context.
The Swastika is commonly seen in India, as it is considered a religious symbol for Hindus, Buddhists and Jains. It is not widely regarded as a symbol for Nazism in India, and in fact, had its origins in Hinduism long before the birth of Nazism, so Western visitors should not feel offended if they see a Swastika in a temple or in the home of a local. It does not mean the person is a Nazi supporter, and does not symbolise anti-Semitism.
The correlation between the Swastika and anti-Semitism is mostly not even understood in India. And in point of fact, India is a land where Jews have lived for thousands of years and always had good relations with their non-Jewish neighbors. It is notable but not surprising, for example, that the local Hindu raja protected the Jewish community of Goa from the Inquisition after the Portuguese captured that port.