I thought 요 was only a verb ending, and my textbook did not introduce adding it to all sorts of parts of speech, which I hear regularly in Korea. From the well-known 저도요 to 이렇게요, noun + 요 etc. Is that actually grammatically correct?
No, you can't add it to everything. For example you can't add it certain (for lack of a better word) 'standard' endings such as (스)ㅂ니다, (십)시오, (으)ㅂ시다, (어/아/여)라, (는)구나, 게, (이)오, and a few things like that.
But you can add it to a lot of things.
By the way, when you add it to a noun, you should use 이요 after a consonsant ending.