No, you can't. The use of も cannot be used to describe two dissimilar things. You could say that Pat has Japanese citizenship and Mark has Japanese citizenship too but not that Pat has Japanese citizenship and American citizenship too.
No, they cannot be negated using じゃないです because たかい and おいしい are not nouns. They are not grammatical and would need to be conjugated differently i.e. たかくないです and おいしくないです.