Salaam & Greeting

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??

Q: Many a time we bump into non-Muslims, either at work, conferences, etc. and they tend to greet with good morning. Is one sinful if he replies to such a greeting by saying good morning back.

Q: I would like to please find out more on mu'aanaqah. Is it a sunnat? Will it be okay to conduct a lesson on it by including it under etiquettes? What is the method of performing it?