How to ask "anybody/anyone/somebody/someone" questions in Chinese?
Basically you want '有人‘ or ’谁‘。

Does anybody know the answer?
有人知道答案吗？
谁知道答案吗？

Someone must know the answer！
肯定有人知道答案！

Does anybody/anyone in the dorm have a vacuum I could use?
我们宿舍有人可以借给我一台吸尘机吗？

"Can I borrow somebody's/someone's shoes?" 
我能借一下别人的鞋子吗？
我能不能借一下谁的鞋子？

May I borrow someone's jacket?
我可以借别人的夹克吗？
我可否向别人借一下夹克？

Who can lend me a jacket?
谁能借我一件夹克衫？

Who can lend me a vacuum cleaner?
谁能借我一台吸尘器？有人可以借我一台吸尘器吗？

（Don't borrow other people's shoes, you might get a foot infection!)