I would like to know if it's okay if i didn't make wudu after taking a bath???

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 .

My question deals with a friend of mine who was ignorantly joking. When my friend was teased by another friend he ignorantly picked up his phone out of joking and said I have to tell Allah. Then he said on the phone "Hello, Allah" as to tell Allah. I know this is incorrect but is this shirk?

What are the most important rights that are respected in Islam?

If one Muslim brother loves another Muslim brother, does he have to say to this brother "I love you for the sake of Allah?

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

Is it true that anyone who does not accept that kuffaar are kuffaar is a kaafir himself, even if he prays, believes in the Qur'aan, and the Prophet Muhammad? If so, what is the proof for this? Can a person insist on believing that Jews and Christians can be believers and go to heaven after being shown clear evidence against this, and still be considered a Muslim?

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?

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

There are many religions.

Why do Muslims think that Islam is true. Is there any factual basis?

I have committed many sins which no one knows of except Allaah. What do I have to do so that Allaah will accept my repentance?