No.1 Something my sister was drawing attracted my attention. I had never seen her draw anthing like it before.
Can I replace "something" with "anything"
Definitely not. You're referring to some (one) specific thing (something).
You can say "Anything my sister draws will be good". This means "It doesn't matter what you choose, if my sister draws it (drew it), it will be good".
and replace "anything" with "something"?
You could almost use 'something' in this context. But "anything" is still much better with a negative, as here.
No.2 Everybody on campus except me knew that the professor had five sets of examinations, which he used in turn.
Can I use "no one" or "nobody" instead of "everybody"?
No, they mean the opposite.
"Everybody knew it" is the opposite of "No one/Nobody knew it".
Looking forward to hearing from you.
Thank you in advance.
Unless I'm missing something vital, both answers a and b are possible.
That's true. I don't think you've missed anything.
For clarification, either word can be used in this sentence, but they mean opposite things. So, in that sense, asking 'Can I use "no one" or "nobody" instead of "everybody"?' is ambiguous. I can see now that jiang probably meant it in the way you've interpreted.