All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The method of the Friday prayer is to perform two Rak'ahs and it is a Sunnah to recite them loudly. It is also a Sunnah to recite in it chapter Al-Jumu'ah [Quran 62] in the first Rak'ah after having recited Al-Faatihah, and to recite chapter Al-Munaafiqoon [Quran 63] in the second Rak'ah after having recited Al-Faatihah as well. As regards reciting chapter Al-Faatihah in the prayer, it is a pillar of the prayer as the Prophet said: “The prayer of a person is not accepted if he does not recite Al-Faatihah.” This is the summary of the method of performing the Friday prayer.
As regards the time of the Friday prayer, we have already issued Fatwa 84549 in which we clarified the opinion of the scholars about it. According to the majority of the scholars it is the time of Thuhr prayer; this time begins when the sun is at its meridian. However, the Hanbali School of jurisprudence is of the view that its time begins when the sun is about an arrow's length high in the horizon after sunrise, which is the time of Dhuha prayer.
Therefore, if the time which you pointed to in the question, is after the sun is at its meridian, then there is no problem in this. However, if this time is before the beginning of Thuhr time, and the people in charge of that country adopt the view of the Hanbali School of jurisprudence, then we think that it is permissible to perform the Friday prayer at this time.
As regards your question whether or not there is a supererogatory (Sunnah) prayer after the Athaan for Friday prayer is given, then the answer is that there is no confirmed Sunnah after the first or second Athaan before the Friday sermon, and it is not confirmed that the Prophet used to perform a supererogatory prayer before the sermon. However, it is permissible for a person who enters the mosque to perform any number of supererogatory prayers he wishes until the Imaam stands on the pulpit. We clarified all this in Fatwa 90213, so please refer to it.