If the menses lasted for over than 9 to 10 days, considered menstruation?

If the duration of the bleeding does not exceed fifteen days, it is all considered menstruation, even if the usual pattern changes.

Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?

The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.

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.

Is hair extension permissible?

All Perfect Praise is due to Allah, The Lord of The Worlds 

It is impermissible for the man and the woman to apply a human`s hair as extension, but using artificial hair is permissible for the married woman after obtaining the approval of her husband so long as non-Mahrams don`t see her. And Allah Knows Best.