We’re not talking about chelek eloka mimaal – that’s a concept that’s discussed everywhere in any machshava sefer that’s after kabalas ha’ari.
Nice try. A piece of godliness placed in a Jewis not the same as saying that specifically a rebbe is the essence of god. Actually, the tanya says there משיח’ שהם בחי’ עקביים ממש לגבי המוח והראש וכן בכל דור ודור יש ראשי אלפי ישראל שנשמותיהם הם בחי’ ראש ומוח לגבי נשמות (that may not have pasted well), that EVERY jew has the chelek eloka, from the avos down to the amhaaratzim; he explains how every part of klal yisroel is compared to higher and lower parts of the body.
The exact opposite of the lubavitcher rebbe’s claim that a tzadik has a special godliness when compared to someone else.
Neither says that you can daven at the graves of a tzadik because a tzadik is the essence of god wrapped in a body.