Some scholars of tajweed said that it is obligatory to read Qur'aan with the rules of tajweed. Is that true?

I want to make my children keen to pray, because they will pray once then forget about prayer many times. I always advise them and pray to Allah to guide them. How can I encourage them and make them love prayer?.

My neighbour is an American Christian, and she and her family brought me a gift when it was Christmas. I could not refuse the gift, lest she be offended.  
Can I accept this gift, as the Messenger (peace and blessings of Allaah be upon him) accepted gifts from kaafirs?

Is it permissible for me to say to non-Muslims "And the same to you" when they wish me a Happy New Year or say Best Wishes?

I have very difficult question and I think this is my only hope that you can help me to find the answer.
I am a Russian Jewish girl and I know this Muslim guy for over a year. The longer we know each other, the more problems and difficulties we face. Not in the religious or cultural ways. We love each other and there is an issue of whether he can marry me or not.
He is a very good Muslim and he comes from traditional family. I am very fond of his beliefs and beliefs of his family. I was born in a very agnostic country and couldn't be properly introduced into any religion. It was forbidden. When I came to the US I started my research on different religions and found out that my beliefs do not really match all Jewish sayings. I did a lot of research on Islam and by looking at him and a couple other Muslim boys and girls, and by reading Quaran, I have a very strong feeling that I could become a good Muslim. I want to go to school to learn the culture and religion more precisely, to learn the language. I contacted the mosque and was ready to go... but I faced the issue: would I be accepted as a Muslim sister like other people who came from different religions except Jewish? Jews and Muslims are in big contradictions and I know that friendship is almost impossible. I am praying to God (in my home language - Russian), to lead me the right way to achieve my beliefs.
Please, help me to find my answers

I am one of those who send blessings upon the Prophet between 50 and 100 times a day, according to circumstances. I say: “Allahumma salli ‘ala Muhammadin wa aali Muhammad (O Allah, send blessings upon Muhammad and the family of Muhammad).” There are some people who tell me that my sending blessings upon the Messenger of Allah is lacking. Can you tell us – may Allah reward you with good – what is the ideal way to send blessings upon the master of mankind, and is the way I am doing it really lacking?

Is it permissible to fast without praying?.

We celebrate the birthday of Prophet Muhammad (peace be upon him). On this day, we read a lot of salutations on him and engage in a lot of prayers to Allah. We try to show our love for our Prophet (peace be upon him). How come you say we cannot do it?
 

I live in a city where there are no other Muslims and no Mosques. I need to peform my friday Jumuah, unfortunately I am not knowledgeable enough to peform the prayer myself, may I use a audio recording to lead me? Also may I use earphones since I don't want to disturb those in the next room and it blocks out distracting noises. I'm studying so that I may peform my own prayers confidently, in the meantime may I use these measures?.

What are the Sunnahs of fasting?.

Is it permissible to pray in a mosque where the ground floor is controlled by the Shi‘ah and the Sunnis control the upper floor?