Is it permissible for a person, who vowed to offer two Rak`ahs(units of prayer) everyday for Allah`s sake, to do so after the Fajr(dawn) prayer?

In principle, a vow should be fulfilled as it was originally intended, and if its time lapses then, it should be fulfilled at any time because of the vow. Therefore, it is permissible to offer them after the Fajr prayer, and there is no prohibition in doing so. However, it is preferable for him to offer these two Rak`ahs at some other time to avoid the disagreement amongst the scholars in this regard.

A Christian woman wants to marry a Muslim man through an unregistered marriage contract and for a specific period because of certain circumstances. She is an adult and wants to know the correct procedure so as not to make any mistakes. What is the correct thing to do in this regard?

I wish I could pray in the mosque, but I know that it is better for a woman to pray at home. I know that the reward for going to the mosque is great, but is this reward restricted to men? I feel jealous of them for that. What should I do ? Is there a way for me to be favored with such reward?

Abdullah Ibin Masood reported that the Prophet (PBUH) said: "Her prayer inside her home is better than its courtyard, and her prayer in her own bedroom is better than inside her home." [Abu Dawood]. Her staying at home, and not going to the mosque in obedience to Allah`s injunctions entails a great reward similar to that bestowed on a man for going to the mosque since the bounty of Allah is for all. And Allah Knows Best.

Is it permissible for the man to go out wearing shorts?

It is permissible as long as his Awrah(private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed.