Can a muslim pray for his non-mulsim mother who has passed away?

Is it permissible to ask the Muslims -when meeting with them- about the state of their faith or their hearts? One of them said to me that this is a matter of the unseen and that it is not appropriate to ask about it.

On some trips there is a Qur'aan reading program, and they divide the people into separate circles (halaqahs) and someone who reads Qur'aan well to correct any mistakes. Is there anything wrong with this?

If the sin involves the rights of another person then what form should repentance take?

When traveling via airplane which direction should one pray? Assuming that due to conditions on the plane the proper direction cannot be ascertained.

What should one who is informed about the correct direction of the qiblah during a prayer?

I forgot that I did not have wudoo' and I prayed. After I finished my prayer, I remembered that. Do I have to repeat my prayer?

How can we teach our children the adhkaar (words of remembrance) to be recited every day and night?

Is it true that the person who is used to studying in Islamic schools, and has no previous experience of studying in non-Islamic schools, will never be able to connect with the environment that surrounds him, where most of the people are non-Muslims and that he will grow up shy and will never find any way to succeed either in his academic life or in the workplace? What is your opinion about that?

What is the Islamic ruling on the issue of imitating the kuffaar in their customs and dealings? What are the guidelines concerning that in Islamic sharee'ah? Is every imitation of the actions of the kuffaar regarded as a haraam kind of imitation, knowing that there are many things that the kaafirs do that are not haraam and are not condemned by sharee'ah, where the one who does them does not do them merely to imitate the kuffaar, but because he thinks those things are good, as Ibn Mas'ood (may Allah be pleased with him) said: "What the Muslims think is good is good before Allah"?  
Please advise us, may Allah honour you, and please give me a detailed answer and explain to me the guidelines on this matter.

I try my best as a Muslim, but my husband says mean things against Islam, I try explaining things to him but he wont listen, he is educated whereas I am not, I do try and learn about Islam from the Quran and sunnah, but Im not perfect, I have 6 children three over the age of 13 and 3 under 9 years. how should I make myslef a better Muslim? and Instill it in my children as the older ones won't pray all they prayers. Sometimes ok most of the time it brings me down.

A woman became Muslim and lives with her family who are not Muslims, and now they do not object to her being Muslim. She tried to call them to Islam by various means, but to no avail. How should she deal with them in their misguided state? Should she uphold ties with them or limit her relationship with them?.