When to Read Surat al-Kahf on Friday
Question

According to the Sunnah, when is the correct time to recite surat Al Kahf on Friday?  Should it be recited after Fajr and before Jumu`ah Prayer or anytime on Friday?  Also, is it from the Sunnah to recite Surat Al-Imran on Friday? And if so, when is the correct time to do so?
Praise be to Allah.Virtues of reciting Surat al-Kahf on Friday
There are sahih ahadith from the Prophet (peace and blessings of Allah be upon him) concerning the virtues of reciting Surat al-Kahf during the day or night of Jumu’ah (Friday). These include: 
(a) From Abu Sa’id al-Khudri, who said: “Whoever reads Surat al-Kahf on the night of Jumu’ah , will have a light that will stretch between him and the Ancient House (the Ka’bah).” (Narrated by al-Darimi, 3407. This hadith was classed as sahih by Shaykh al-Albani in Sahih al-Jami’, 6471) 
(b) “Whoever reads Surat al-Kahf on the day of Jumu’ah, will have a light that will shine from him from one Friday to the next.” (Narrated by al-Hakim, 2/399; al-Bayhaqi, 3/249. Ibn Hajar said in Takhrij al-Adhkar that this is a hasan hadith, and he said, this is the strongest report that has been narrated concerning reading Surat al-Kahf. See: Fayd al-Qadir, 6/198. It was classed as sahih by Shaykh al-Albani in Sahih al-Jami’, 6470) 
(c) Ibn ‘Umar (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Whoever reads Surat al-Kahf on the day of Jumu’ah, a light will shine for him from beneath his feet to the clouds of the sky, which will shine for him on the Day of Resurrection, and he will be forgiven (his sins) between the two Fridays.’”
Al-Mundhiri said, this was narrated by Abu Bakr ibn Mardawayh in his Tafsir, with an isnad with which there was nothing wrong. (al-Targhib wa’l-Tarhib, 1/298) 
When to read Surat al-Kahf on Friday?
Surat al-Kahf may be read during the night or the day of Jumu’ah. The night of Jumu’ah starts from sunset on Thursday, and the day of Jumu’ah ends at sunset. Therefore the time for reading this surah extends from sunset on Thursday to sunset on Friday. 
Al-Manawi said:
"Al-Hafiz ibn Hajar said in his Amali: “In some reports it says ‘the day of Jumu’ah’ and in some reports it says ‘the night of Jumu’ah’. They may be reconciled by saying that what is meant is the day which includes the night and vice versa.” (Fayd al-Qadir, 6/199)  
Al-Manawi also said:
“It is recommended to read it during the day or night of Jumu’ah, as al-Shafi'i (may Allah have mercy on him) stated.” (Fayd al-Qadir, 6/198) 
Should we recite Surat Al `Imran on Friday?
There are no sahih ahadith concerning reading Surat Al ‘Imran on Friday. All the reports that have been narrated concerning that are either da’if jiddan (very weak) or mawdu’ (fabricated). 
Ibn 'Abbas said: “The Prophet (peace and blessings of Allah be upon him) said: ‘Whoever recites the surah in which the family of ‘Imran (Al ‘Imran) are mentioned on Fridays, Allah and His angels will send blessings upon him until the sun sets.’” (Narrated by al-Tabarani in al-Mu’jam al-Awsat, 6/191; and al-Kabir, 11/48. This hadith is da’if jiddan (very weak) or mawdu’ (fabricated)). 
Al-Haythami said, “This was narrated by al-Tabarani in al-Awsat or al-Kabir, and it [its isnad] includes Talhah ibn Zayd al-Riqqi, who is da’if (jiddan) ((very) weak).” (Majma’ al-Zawaid, 2/168). 
Ibn Hajar said: Talhah is very weak, and Ahmad and Abu Dawud accused him of fabricating reports. (See Fayd al-Qadir, 6/199) 
Shaykh al-Albani said: (it is) mawdu’ (fabricated). See hadith no. 5759 in Da’if al-Jami’. 
And al-Taymi narrated in al-Targhib that “Whoever recites Surat al-Baqarah and Surat Al ‘Imran on the night of Jumu’ah will have reward like that which is between the seventh earth and the seventh heaven.”
Al-Manawi said, it is gharib da’if jiddan (strange and very weak).(Fayd al-Qadir, 6/199) 
And Allah knows best.