1) Recently, my wife had a conversation with another sister. The sister informed my wife that she was going to be doing some long distance traveling to visit some of her relatives. This sister is married and she will be traveling without her husband. My wife expressed a concern to me. In addition, I was not too sure if I should remind the brother about his responsibility to be his wife's mahram. Could you remind us what is the proper ettiquette of traveling in this situation? Whatis the sunnah of traveling? When can the husband not have to travel with his wife? Also, should I remind the brother about his responsbility of being a mahram OR would I be overstepping my bounds in approaching him as fear of causing a negative situation. You see, some Muslims do not like to be reminded of these type of things and become angry. Thus, causing a harm in the relationship.
A woman may not travel at all without a Mahram. This is a clear command from the Prophet 
. However, in some cases, if you see someone doing wrong, it is not easy to stop him or advise him. You have to exercise wisdom, patience, etc. You can refer to our book: "Commanding Good and Forbidding Evil" to get a better understanding of this issue.
2) Recently, I had a discussion with a brother about the issue of a mahram. I informed him that a woman cannot travel without a mahram because of the following evidences:
told him "Go and perform Hajj with your wife."
Both ahadeeth can be found in Bukhari and Muslim and Riyadh-us-Saliheen under the Etiquettes of Traveling.
The brother informed me that there are exceptions to this rule. Are you familiar with these exceptions?
No.
3) What is the minimum that someone can travel before having to pray Qasr? I have heard 3 miles, but that seems too little.
If a person is going out on a travel-trip, then once he departs from his hometown's buildings, he can start making Qasr, and can continue doing so until he comes back. A travel-trip is defined as a trip where one prepares for his trip as a traveller would, and where it is commonly understood by the people that the distance he is travelling is a travel (as opposed to residence) distance.
4) In reference to the following hadiths, please clarify some for me please
Abdullah ibn Umar SAHIH AL-BUKHARI 2.192 The Prophet (peace be upon him) said, "A woman should not travel for more than three days except with a Dhu-Mahram (i.e. a male with whom she cannot marry at all, e.g. her brother, father, grandfather, etc.) or her own husband."
AbuHurayrah SAHIH AL-BUKHARI 2.194 The Prophet (peace be upon him) said, "It is not permissible for a woman who believes in Allah and the Last Day to travel for one day and night except with a Mahram."
AbuSa'id al-Khudri SAHIH AL-BUKHARI 2.288 Qaza'ah Mawla of Zayd said, "I heard AbuSa'id al-Khudri narrating four things from the Prophet (peace be upon him) and I appreciated them very much. He said, conveying the words of the Prophet (peace be upon him), "(1) No woman should travel on a journey of two days except with her husband or a Dhu-Mahram.
1.These hadith "appear" to imply that a woman may not travel for more than a day, up to three days. Does this mean that if a woman takes a plane from Florida to New York Approximaly 5 hour flight to see her mother because her husband can?t or won?t go with her that she is never allowed to see her mother even though the hadith appears to imply that one may not travel for more than a day?
2. Why do these hadith appear to give different times frames for allowance of traveling, if a woman is never allowed to travel alone?
3. In a case were a husband has gotten a job in Saudia Arabia, but the company's rules are that he may not bring his wife for 6 months to Saudia Arabia, when the six months are up is it permissible for her to fly to Saudia alone, or must he come back to get her? If he is unable to take the time off work to come back and get her, should he quite the job and come back to the U.S. or should she stay at the U.S. and wait up to 1 year when he can come and get her?
4. If a woman's husband has gone over sees for one month to visist his family or to look for a job, must the woman stay in her home, may she drive from Virginia to Penssilvian to stay with another sister if she does not have mahram.
5.Concerning conventions, many sisters want to attend conventions in which there husbands can?t or won?t attend. If a woman man not travel alone then would it be a good idea to note this on your registration applications for those women who are not aware of this, because no one would want to receive a bad deed on their record to attending a convention. (Perhaps on convention applications it should read Women who do not have a mahram to travel with them if then are not living within X miles of the convention sight may not apply for registration)
There is one more authentic hadith that does not specify a period, making the ruling general and applicable to any travel. According to some scholars, the periods have been mentioned in some of these reports according to the special occasion where the hadith was said, such as, for instance, a woman wanting to travel 3 days without a mahram, and his answer referred to the 3 days, etc.
If a woman is in a situation where it is necessary for her to travel without Mahram, then necessity makes prohibitions permissible. Seeking the knowledge can sometimes be a necessity. But one should not be inclined to consider everything a necessity. Allah knows for sure whether a certain matter is necessary for us or not.
5) I am planning to travel to Mecca with my wife to make umra during Ramadhan and I am not sure when to fast and not to fast during the travel. Could you please help me to understand if I should break the fast during the plane flight, during travel from Mecca to Madina, or the return flight since I am not staying the entire month.
You may fast the whole period, and you have the option of breaking your fast whenever you travel and make it up later. It all depends on your physical ability.