The correct passive form of the given sentence is Many toys in the shop were broken by the child. Even the paintings were thrown by him.

The active voice of the sentence is The child broke many toys in the shop. He even threw the paintings. This sentence is in the simple past tense, which is used to describe an action that happened in the past. The passive voice of the sentence is formed by putting the subject of the active sentence after the verb "to be" and the past participle of the main verb. In this case, the subject of the active sentence is "child" and the main verb is "break." The past participle of "break" is "broken." So, the passive form of the sentence is Many toys in the shop were broken by the child. Even the paintings were thrown by him.

The other options are incorrect because:

• Many toys in the shop have been broken by the child. Even the paintings were thrown by him. is also in the past perfect tense, but it implies that the toys have been broken multiple times.
• Many toys in the shop were broken by the child. He has even thrown the paintings. is in the past perfect tense, but the action of the paintings being thrown happened at the same time as the action of the toys being broken.
• Even the paintings have been thrown by the child. is missing the subject of the sentence. The subject of the sentence is "paintings."
• Even the paintings were thrown by him. is missing the main verb. The main verb of the sentence is "throw."