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 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. And Allah Knows Best.
I prayed all the obligatory prayers in congregation, but after finishing the `Isha prayer, I remembered that I had forgotten to pray Dhuhr. What should I do, and is my prayer invalid?
Your prayers are valid, but you must make up the Dhuhr prayer as soon as you remember it, based on the saying of the Prophet (peace be upon him): "Whoever forgets a prayer must pray it as soon as they remember it; there is no expiation for it except this." [Muslim]. And Allah knows best
Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?
There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj,vol.3/pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.