Is photography forbidden, such as photographs of children?

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 it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?

It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).

Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?

It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.