Salaam & Greeting

Q: If someone gave salaam and one replied and they didn’t hear the reply or one did not reply, would the person later on have to walk up to the person and reply?

Q: Whilst my father was abroad, if he asked me to give salaam to the congregants at the masjid and I said I would Insha’Allah thinking that I would approach the Imam to tell everyone but I didn’t do so and my father asked me more than once and I didn’t do so on any occasion, as my father is back now, what would I do?

Q: I wanted to know if a female can say Assalaamu alaikum to a male non mahram and vice-versa?

Q: Which greeting can we use for non-Muslims? If we say Assalaamu Alaikum, we cannot pray for them in this way. If we say good morning, we are promoting Christianity greetings. So how should we great non-Muslims?

Q: Can we say salaam to a kaafir or can a kaafir say salaam to us?

Q: Is it ok to just say سلام عليكم? In Hayaatus Sahaabah (Part 2), under chapter 9 -

خروج الصحابة رضي الله عنهم من الشهوات - :التسليم على المسلم - عمل ابي امامة رضي الله عنه في ذالك

A riwaayah comes wherein Abu Umaamah رضي الله عنه said this.

Q: I have been advised to omit the salaam when sending out a wake up for fajr reminder. The sender says those who do not respond will be deemed to be sinful. Kindly advise. 

Q: How can I write the salaam? I mean "As-salamu alaikum" in a proper way in English. Nowadays most people are writing salaam in English in different ways. Please explain whats the correct and incorrect way.

Q: Is it permissible for a Muslim to initiate the greeting with a kaafir, e.g. good morning?

What if this is for the purpose of inviting people to Islam?

Q: Two people are entering a house. The first person who enters says assalaamu alaykum. Should the second person who enters say wa alaykumus salaam, in response to the first persons salaam or should they say assalaamu alaykum as we learn is the etiquettes of entering a house??