金山词霸牛津字典在线的例句：
used to give the following word or phrase a negativemeaning, or to reply in the negative （否定后面的词或短语，或作否定的回答）不，没
He warned me not to be late.
他提醒我不要迟到。
I was sorry not to have seen them.
我非常遗憾没见到他们。
Not everybody agrees.
不是每个人都赞同。
‘Who's next? ’ ‘Not me. ’
“下一位是哪个？”“不是我。”
‘What did you do at school? ’ ‘ Not a lot . ’
“你在学校做什么了？”“没做多少事。”
It's not easy being a parent .
为人爸爸妈妈真困难啊。
used after hope , expect , believe , etc. to give anegative reply （用于hope、expect、believe等动词后，作为否定的回答）不，没
‘Will she be there? ’ ‘I hope not. ’
“她会在那儿吗？”“但愿不会。”
‘Is it ready? ’ ‘I'm afraid not. ’
“筹备好了吗？”“恐怕还没有呢。”
‘Does he know? ’ ‘I believe not. ’
“他知不知道？”“我想他不了解。”
or ~ used to show a negative possibility （表示否定的可能性）否，可能不
I don't know if he's telling the truth or not.
我不了解他是不是说了真话。
used to say that you do not want sth or will not allowsth （拒绝或不允许）不
‘Some more? ’ ‘Not for me, thanks. ’
“再来点儿吗？”“我不要了，谢谢。”
‘Can I throw this out? ’ ‘Certainly not. ’
“我把这个扔了，行吗？”“当然不可以。”
韦氏字典例句：
In the word “macho” the “ch” should be pronounced as in “China,” not as in “Chicago.”
在单词macho中，ch的发音应该和在单词China中一样，不应该是Chicago中的发音。
我的疑问1：否定后面的词或短语，或作否定的回答，我感觉还可以否定后面的完整的句子（参见韦氏字典的例句）
我的疑问2：
像Is it ready? ’ ‘I'm afraid not.如此的句子都有not的对象这里是相反的ready。那样
‘Some more? ’ ‘Not for me, thanks. ’这里Not否定的是什么？
‘Can I throw this out? ’ ‘Certainly not. ’这里not否定的是can还是throw呢？
What did you do at school? ’ ‘ Not a lot .‘这里not否定的又是是什么，貌似这个Not a lot答非所问？
我看你的问题中，不少都可以看作为省略形式的回答或表达，以防止重复。
疑问1：否定后面的词或短语，或作否定的回答，我感觉还可以否定后面的完整的句子（参见韦氏字典的例句）
答：可以如此理解。如： In the word “macho” the “ch” should be pronounced as in “China,” not as in “Chicago.”
not as in “Chicago= but should not be pronounced as it is in Chicago.
疑问2：（问题省略）
答：Is it ready? ’ ‘I'm afraid not. = I'm afraid it is not ready.
Can I throw this out? ’ ‘Certainly not. =you certainly cannot throw it out. can只是谓语动词的一部分，否定含义当然包括throw了。
如：I cannot speak English. 你感觉能不否定speak English吗？即便中文里，假如你说不可以，后面要加动词的，不可以什么？
除非是省略句，在上下文了解的状况下才能。
What did you do at school? ’ ‘ Not a lot.以这里的not a lot 是习语，意思是“没做什么”。
请看字典例句：
A: "Hey, Tom, it's been a while since I last saw you. What have you been up to?"
B: "Oh, not a lot. Still in the same job."
https://idioms.thefreedictionary.com/not+a++lot
