India's not a house, so yes. It can be a "home".

The word यह transforms to इस when there is a postposition like में, पर, के साथ etc. (Same with वह to उस, ये to इन and वे to उन.) The appropriate example would be इस सेब के साथ नाश्ता करो (Have breakfast with this apple).

You have changed the word order, and therefore the emphasis. Until they can add in other alternatives, it is always best to stick to the correct order.

House (the actual building) would be makaan, while home is ghar. If you are referring to the literal house, they are interchangable, but you wouldn't describe the larger area where someone lives as their house.

House refers more to a construction than the sentiment. Perhaps house is wrong because elephants tend not to construct permanent structures.