So can shaving around neck area cause lymph nodes to swell up and down? Crevicle and chin nodes.

Prob not. While shaving can cause minor cuts in the skin, and therefore theoretically increase risk of a skin infection, which could lead to some swollen lymph nodes, this is not common. (you should wash your face before shaving). If you're saying someone has multiple enlarged lymph nodes from their chin down to their clavicle, i would recommend they see their doctor for an evaluation.