Last Sunday I climbed to the top of the hill near my home,where I could see half of the city这里的先行词是，near my home这个介词短语作状语？还是名词the top of the hill。 那么在这句中，I made friends with Tom during his stay in Beijing,which he was studying Chinese in a university.这里的先行词是不是his stay in Beijing，这里是时间状语吗？不是说定语从句的先行词只是名词和代词吗
第二个句子本身是错的，不能用which，单独用which是要充当主语或宾语的，he was studying Chinese in a university 这里主谓宾齐全，非要用which要在前面＋during，变成during which，要么直接用when。非限定性定语从句的先行词可以由短语或整个句子充当。这里应该是during his stay。
你可以去百度一下的你的句子，出问题了，我看到的是I made friends with Tom during his stay in Beijing, when（或者during which ） he was studying Chinese in a university there. 这个应该才是正确的。
第一个句子中， 出现的介词短语near my home其实是对the top of the hill负责，the top of the hill才是中心词，所以the top of the hill才是先行词。
第二个句子中， during his stay 和 in Beijing 两个介词短语，我们可以先假设先行词是in Beijing，带入从句中会发现意思会有重复， 其实句子中的there 已经指代了in Beijing， 所以先行词只能是during his stay。
两个句子的讲解其实代表了两种思路，一种是能直接看出介词短语真正对谁负责，如果看不出可以用代入法排除。
这里再举两个例子理解非限制性定语从句
限定性定语从句的先行词只能是名词或代词，而非限定性定语从句的先行词则可以是名词或代词，也可以是短语或句子；另外，当先行词为专有名词或其他具有独一无二性的普通名词时，通常要用非限制性定语从句，而不用限制性定语从句。
如： Peter drove too fast, which was dangerous. 彼得开车很快，这是很危险的。(which指drive too fast)
He changed his mind, which made me very angry.他改变了主意，这使我很生气。(which指整个主句)