Sir, I have listened the opinion of Sheikh Salah Al Munajid. He said on islamqa.com,
“There is nothing wrong with congratulating one another at the beginning of the month. The Prophet (peace and blessings of Allaah be upon him) used to tell his Companions the good news of the onset of Ramadaan, and urge them to make the most of it. Abu Hurayrah (may Allaah be pleased with him) said:
The Messenger of Allaah (peace and blessings of Allaah be upon him) said,
‘There has come to you Ramadaan, a blessed month. Allaah has made it obligatory on you to fast (this month). During it the gates of Paradise are opened and the gates of Hell are locked, and the devils are chained up. In it there is a night that is better than a thousand months, and whoever is deprived of its goodness is deprived indeed.’” (Reported by al-Nisaa’i, 4/129; Saheeh al-Targheeb, 1/490)”
But, the hadiths about the fazilat of Juma are also present but that’s a bid’ah.
If there is a narration from the companions that they ever Muhammad(saw) or his companions did this. Then, I can agree otherwise I can’t blindly follow any Sheikh.
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The hadeeth, though it is weak but scholars have used it a lot.
What is authentic is that the Salaf used to great each other in Eids.
Scholars, like Ibn Al Qayyem said that whoever has a new worldly blessing from Allah, it is permissible to greet him and congratulate him for it. however, religious blessings are more worthy.
As for Friday, I don’t know any of the scholars who said that it is permissible.
As for “otherwise I can’t blindly follow any Sheikh.”, this is up to you if you are a student of knowledge and know Arabic well. if not, you are following your Sheikh blindly because you depend on his translation!