The question "can I have any milk" may inquire whether the asker is able to have any of various kinds. If it was a polite question asking permission, then I would agree that "some" is the right answer. That is "could I have some milk?" In the case of "are there any apples", the inquiry relates to whether a supply of apples is available or not. I hope this helps.

你要弄明白一个问题，就是：到底这个卷子是谁出的，如果是中国人出的，你就要选择b 。要是老外说的，你就要怀疑一下，这是不是真的老外。就像我在网看到的：‘您好！吃了吗？’ 最有可能发生什么场合， a：厕所，b 澡堂子，c ： 胡同口 细想起了，其实是一个道理

A little lagniappe…A small comment on the first sentence in your example. Those of my generation were taught strict grammatical rules. “Can” denoted physical or mental ability and “may” denoted permission or authorization. It wasn't OK to use “can” if you were talking about permission. Today many grammatical rules are ignored and people generally use “can” in everyday speech to denote permission. However, in situations where one is expected to be polite we use “may” to denote permission.

Can I have any milk? Are there any apples? No,There're not any apples. Could I have some milk? Yes, you can/No ,you can't. 一般来说，在疑问句和否定句中用any,在征求意见的疑问句中用some.

The answer to the first question is ：A The answer to the second question is：your