個人課外教師

1. Is と needed in this sentence? This is a machine translation, so I'm not sure.
2. Is 個人課外教師 correct to mean "a private tutor"?
3. Is マンツーマン correct to mean "one-on-one"?

この文章で「個人課外」とは、個人課外教師から受ける授業を意味します。 マンツーマン方式なら「個人課外」と言い、数人をまとめて教える方法は「グループ課外」だと言います。

1. I don't suppose it's required exactly, but it's a normal way of discussing the meaning of a word or phrase.
2. I don't think it's incorrect, but 家庭教師 and 個人教師 are the usual terms. 個人課外教師 may be trying to say something more specific.
3. Yes. It's a direct loan word from the English "Man to Man".