“Signed up” is a phrasal verb. Our post Phrasal Verbs explains that when you are using transitive phrasal verbs, some can be separated and some cannot. In a phrasal verb that can be separated, the object can appear either between the main verb and the particle or after the phrasal verb’s components. Since “signed up” can be separated, either sentence is grammatically correct.

I have signed up my daughter for this class.
I have signed my daughter up for this class.

“For….dollars” is a prepositional phrase (see What Are Prepositional Phrases?). There are no “adverbs of quantity/measure” in American English. The sentences “The book costs 20 dollars” and “I weigh 65 kilos” do not contain any adverbs. See our post Numbers as Adjectives.

In English only the pronouns “me,” “him,” “her,” “us,” and ‘them” are in the accusative. The accusative case is rarely referred to in English but is pervasive in a language such as German.

In that case is “for ….dollars” in the accusative case? I mean according to this defintion: “the accusative, or the accusative case,” is the case used for a noun when it is the direct object of a verb, or the object of some prepositions.”

The direct objects of the verb “buy” are “magnets” and “hooks.” The object of the preposition “for” is “dollars.”