Firstly: 

Yes, it is proven from the Prophet (peace and blessings of Allaah be upon him) that he said: “Whoever regularly prays four rak'ahs before Zuhr and four after it will be forbidden to Hell.” Narrated by Abu Dawood (1269) and al-Tirmidhi (428); classed as saheeh by al-Nawawi in al-Majmoo’ (4/7) and al-Albaani in Saheeh Abi Dawood. 

Secondly: 

There is no Sunnah prayer before Jumu’ah prayer, because that is not proven from the Prophet (peace and blessings of Allaah be upon him) and there is no report from the Sahaabah (may Allaah be pleased with them) that suggests that there is any specific regular Sunnah prayer before Jumu’ah. Rather it was narrated that naafil prayers in general may be offered, without specifying any number. 

This has been discussed in the answer to question no. 6653 and 14075. 

It is not valid to draw an analogy between Jumu’ah and Zuhr prayer and say that it is mustahabb to offer the regular Sunnah prayer before Jumu’ah as it is mustahabb to do so before Zuhr, because Jumu’ah prayer is different from Zuhr prayer in many ways, and because this analogy is contrary to the apparent Sunnah of the Prophet (peace and blessings of Allaah be upon him), which is that he did not offer any regular Sunnah prayer before Jumu’ah. The best guidance is the guidance of the Prophet (peace and blessings of Allaah be upon him). If the Prophet (peace and blessings of Allaah be upon him) had offered any prayer before Jumu’ah, that would have been narrated to us. As there is no such narration, we know that he (peace and blessings of Allaah be upon him) did not offer any regular Sunnah prayer before Jumu’ah. 

With regard to praying after Jumu’ah, a number of ahaadeeth concerning that have been narrated from the Prophet (peace and blessings of Allaah be upon him). We have discussed that in the answer to question no. 112031. 

And Allaah knows best.