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.

就近原则就是动词或be动词前不管有多少东西只要它前一个单词（词组）是单数，你就用单数，是复数你就用复数，你举的例子第一句是对的因为she是第三人称单数

应该是Her friend and she like to go shopping. 这里的and 是并列连词，不能用就近原则。
以下用就近原则：Either you or she likes going shopping.
Neither you nor she likes going shopping.
...

就近原则动词的形式要与靠近它的名词一致。
应该是这一个 her friend and she likes to go shopping.