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

How should we call people to Islam?

 As-salamu `alaykum. I work in a software company where the dress code is business formal. So, it’s compulsory to wear shoes. The thing is I have to remove my socks and shoes every time I make wudu’. I heard that it’s not necessary to remove socks for wudu’. Well, I'm not sure about that and its procedure. So, if there is any alternative to this, then, please, enlightenment me on this. Jazaka Allah khair.

What is the ruling on fasting six days of Shawwaal? Is it waajib (obligatory)?

I have a question regarding dawah. I am tring to convince my muslim brothers to do dawah to non muslims but hey said that we should fix the muslims first because muslims dont pray etc and so there argument was that is it better to halve a thousand workers in a company and improve them or to get a thousand more, So is dawah fard .

There was a discussion about the issue of putting one’s trust in Allah (tawakkul) and taking measures; the trust of some of the righteous is like that of Maryam, to whom summer fruits used to come in the winter and vice versa without her taking any measures; rather she focused completely on worship. Please advise us about that, may Allah bless you.

What is the ruling on one who delays Hajj for no reason when he has the means and is able to do it?

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?.