"That child does not like cheese."
Translation:To dítě nemá rádo sýr.
No, rád is a special case, an exception. It is an adjective, but it has an adverbial meaning and it exist only in the nominative form. Singular rád, ráda, rádo, plural rádi, rády, ráda.
Many adjectives have nominative (also called "short") forms, but they are bookish or archaic. rád is an exception, because it has only the nominative forms and it has the adverbial meaning.
All other nouns or adjectives keep the usual rules after mít. The direct object of mít is in the accusative case.
No, it is hard to translate it directly, but if anything, it would be closer to "glad". It is similar to German "gern".
I do not know where you read that, but you are probably not interpretting it correctly. chutná mi means it tastes well (right now) but can also be used that you like the taste in general. mám rád is I like (in general).