With regard to du'a for entering the house, one should mention the name of Allah, remember Allah and give the greeting of salaam, even if there is no one in the house. For more, please see the detailed answer.

There is nothing wrong with responding when a non-Muslim greets a Muslim at Eid or on any other occasion, by wishing him well and praying for him in an appropriate manner that is equivalent to his greeting. So one may say to him, “May Allah help you” or “May Allah honour you” and the like, and if the intention is to pray that Allah bless him and guide him to Islam, then that is more appropriate and better. And Allah knows best.

Scholars differ as to whether there is a difference between hamd and shukr. Some maintain that hamd and shukr mean the same thing. While others view that hamd and shukr are not the same. Please see below.