Girl uncovering her hair when a boy comes to propose

Q: We follow a practice in the case of a marriage proposal that first the boys mother comes to see the girl, then both parties make itikhara, if positive, then we go for investigation, meet the boy personally and thereafter when everything appears to be positive, the girl and the boy are shown to each other face to face. My question is that when the girl is shown to the boy after all other steps are done, can she show her hair or uncover her head in front of the boy only with whom she is being proposed to marry?

Mocking someone with a beard

Q: A man started keeping a beard after shaving for a long time. He is a Muslim. My father told me that "to be true he was looking better before"(because that man doesnt really look good after he started keeping a beard) I also agreed with my father saying that he was looking good before because when a man leaves his beard after shaving it for long time, he does not look good but after the beard grows he looks good. I had seen another man (who is a Muslim) who had shaved for a long time then left his beard and he too was not looking good but now he is good looking because of a big beard?

My question is that: Is there any affect on us being Muslims? Because we said that a man is not looking good while he was obeying Allah and His Messenger (sallallahu alaihi wasallam) by leaving a beard.

Mocking Islamic teachings

Q: A boys birthday was on December 26 and I said to him that it was better if it was on new year.

Now my question is that I supported new year and I supported something haram (by saying that it was better if it was on new years day). I rejected Allah's rule and supported something haram.

1. Does it affect me as a Muslim? If yes what to do?

A boy said to me that celebrating birthdays is haram and I said that celebrating new year is also haram. Then I said that haram cancelled a haram as we do in maths where a numerator and denominator cancel eachother. Then I laughed and the the boy laughed too.

My question is that I made fun of Islamic rules by cancelling the haram of it in a funny way. I read in a place that making fun of Islam leads to a person becoming a kafir. Is it right? and does it have any affect on mmy imaan?