Reciting the Prophetic narration is permissible as many scholars used to, since in principle, the rulings of recitation have to be observed while speaking Arabic language.

Is it permissible for me to make up for my late father`s missed fasts, and should I make an intention to this end by saying: “I intend to make up for my late father`s missed fasts .”

It is permissible to fast on behalf of the deceased father in order to make up for his missed fasts, and you should make the intention for offering fast from night time, but uttering the intention isn`t a condition.

Is Zakah(obligatory charity) due on the equipments used in the trading process such as: cars , shops etc..?

No Zakah is due on equipments used in the trading process such as cars and the like.

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.