What is the ruling on eating and staying in a Hindu home, taking into consideration that the food is halal and cooked in a halal manner, and if they display some of their rituals? And does the impermissibility of that contradict respecting their feelings and opinions?

It is permissible for a Muslim to eat food from non-Muslims, other than their slaughtered animals. As for their slaughtered animals, only those slaughtered by the People of the Book are permissible. It is permissible to eat with a disbeliever, as long as they are not belligerent, and this may even be an act of righteousness. It is not permissible for a Muslim to sit in gatherings where rituals and ceremonies of disbelief are performed. The opinions that must be respected are those that do not contradict the Book of Allah and the Sunnah of His Prophet; it is not an act of respect to remain silent about evil. A Muslim deals with non-Muslims with justice and kindness, and desires their guidance.