Differences between 谁都, 哪儿都, 什么都?
Your sentences are correct. 谁都 has something to do with people, and therefore everyone. 哪儿都 has something to do with locations, and therefore everywhere. 什么都 has something to do with things, and therefore everything.

Although you have your sentences correct, I have to say be careful with the affirmative and the negative versions. If you use 谁都+没, then it should beno one. If you use 哪儿都+没, then it should be nowhere. If you use 什么都+没, then it should be nothing or anything.