How can I repent from encouraging my neighbor to abandon some religious duties, such as growing a beard, and telling him the Hadith: "Indeed, this religion is firm, so penetrate it gently, gently"? And must I correct what I told him immediately despite the embarrassment and distance, or is it permissible to delay that?

May Allah reward you for your eagerness to correct the mistake. You can make contact to discuss general topics and guidance, advising your friend regarding his distance from his religion and his observance of prayers. Then, during that conversation, you can address the truth concerning the aforementioned hadith in the question, without mentioning the old discussion.