Is it incumbent on a husband to pay the alimony of his wife if she had left him and stayed at her parent`s without his permission?

When a wife leaves her house, and stays at her parent`s without asking her husband, she is considered a Nashiz (wife who refuses to abide by her husband’s orders), and so she doesn`t deserve an alimony.

What is the Time for Making up Fajr Prayer and Other Missed Ones?

I suffer from chronic asthma which requires ventoline inhale; which is an air causes the risperatory track/airways to expand. Am I permited to use it during the daylight of Ramadan? And does break one's fast? Noting that I can't go an entire day without using it?

Taking inhaler through the mouth or the nose breaks one's fast, because it is meant to reach the lungs which are part of the coelom. Therefore, whosoever use inhalers for couple of days is obliged to preserve his fasting and make up that day later. As for the ones the ones who need to use it every days are obliged to preserve his fast and feed a poor per day and the cost of feeding one poor is estimated (60) piasters for the year (1421AH). And Allah Knows Best.  

Is a wife considered sinful if she asked for divorce because her husband married another woman?

A second marriage is lawful, and so it is impermissible for you to ask for divorce because of that. If you are certain that you won`t be able to deliver Allah`s rights and those of your husband`s , then it is permissible for you to ask for Khul`a (Divorce on the demand of the wife). However, you should exercise patience since after difficulties, there is easiness by the will of Allah.