her friend and i like to go shopping.

你不必把问题复杂化了.一般情况下,出现有可供选择的主语时,才使用就近原则.给你两个例子,He or you are wrong. Neither we nor she is correct.
只要出现and,肯定是1+1等于2,当然就成了复数,就要用复数动词了.因此,理应是：
Her friend and she like to go shopping.
但是,你这里又违反了一条原则,第三人称的排列语序往往是：
She and her friend like to go shopping.
如满意,敬请适当给分,以尊重解答者的劳动.为争取获得较高水平的答案,也建议适当出分悬赏.