Is the Hadith: "The Muslim's right over another Muslim is five: returning the salaam, visiting the sick, following funerals, accepting invitations, and responding to one who sneezes" authentic, and to what extent is the narration by Muslim authentic: "The Muslim's right over another Muslim is six: when you meet him, greet him with salaam; when he invites you, respond to him; when he seeks your advice, advise him; when he sneezes and praises Allah, respond to him; when he falls ill, visit him; and when he dies, follow his funeral"?

Yes, this hadith is authentic. In Sahih al-Bukhari, it is narrated from Abu Hurairah that the Messenger of Allah, peace and blessings be upon him, said: "The rights of a Muslim over another Muslim are five: returning the salam, visiting the sick, following funerals, accepting invitations, and responding to one who sneezes." And in Sahih Muslim, it is narrated from him, peace and blessings be upon him, that he said: "The rights of a Muslim over another Muslim are six: when you meet him, greet him with salam; when he invites you, accept his invitation; when he seeks your advice, advise him; when he sneezes and praises Allah, respond to him; when he falls ill, visit him; and when he dies, follow his funeral."