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

I am from a Muslim background, but I never used to offer the obligatory prayers and even when I tried to pray once, I did not do it right. In other words I did not prepare to do it in the proper manner. I ask Allah to forgive me. I heard that the one who does not pray is a disbeliever and is not a Muslim, but whoever offers the five daily prayers, or one or two of them and omits the rest, is regarded as a Muslim. Also, I did not pay zakah on my wealth, but for at least two years I have completed the fast of Ramadan, and I intend to continue doing so. I want to learn how to pray and make it part of my life, along with other acts of worship. 

Is it obligatory for me to pay zakah for all these many years (when I did not pay it), and to make up the days that I did not fast at the time when I was not praying? 

Please note that I have now reached the age of thirty-one years; perhaps you will understand that this may cause me a great deal of hardship; to ward off that hardship, can I start over? Will Allah forgive me if I do that?

I have a question about some terminology that I would like you to explain to me. In some audio lectures I hear words such as (a marfoo' hadith) or  (a maqtoo' hadith)..

I don't celebrate Christmas in any way, but my 11 year old daughter loves the beauty of a Christmas tree when decorated. Is it permissible for me to have one in my house throughout the year?

Question:

I have a few questions concerning parents
1-What right does my Mother have over me?
2-What right do I have over my mother?

If a man decides after a life of sinfulness to come to God and promise to reform his life, I understand that Islam says that he will be forgiven and therefore inherit the promises etc.
My question though is what has happened to the weight of this man's sin, as in sinning he has offended God and therefore this sin has to be atoned for; who is going to atone for his sin, if God is just going to forgive him on the promise of his being good and faithful? Surely as we saw with Adam there has to be a consequence for sin...

Who do Muslims worship?

Can you recommend a book in english that explains what it really means that the Qu'ran is not a creation; and what we should believe in as Muslims?

I have heard that there is a certain attitude that the Muslim should adopt if he faces a time of fitnah (tribulation). What is the attitude towards fitnah?.

Is it valid to read Qur’aan from the computer instead of from the Mushaf ?
In other words, reading from websites on the Internet or from text files that contain the entire Qur’aan, which is displayed on the computer screen. I work in a company and during my breaks I read Qur’aan on the computer.
Is it necessary to have wudoo’ for this kind of reading, as is the case when reading from the Mushaf?.