From Abu Hurairah who said: "The price of a dog was prohibited, except for the hunting dog."

This Hadith is not correct from this route. Abu Al-Muhazzim's name is Yazid bin Sufyan, and Shu'bah bin Al-Hajjaj criticized him and graded him weak. Similar to this has been reported from Jabir, from the Prophet (ﷺ), but its chain is also not correct.
Jami` at-Tirmidhi Book 14, Hadith 83
← Previous Hadith "The Messenger of Allah (ﷺ) prohibited eating the cat and from its price."

This Hadith is Gharib. We do not know of any major (known) narrators who reports from 'Umar bin Zaid (one of the narrators) besides 'Abdur-Razzaq.

Jami` at-Tirmidhi Book 14, Hadith 82 Next Hadith → That the Messenger of Allah (ﷺ) said: "Do not sell the (slave) female singers, not purchase them, nor teach them (to sing). And there is no good in trading in them, and their prices are unlawful. It was about the likes of this that this Ayah was revealed: And among mankind is he who purchases idle talk to divert from the way of Allah."

There is narration about this from 'Umar bin Al-Khattab.

We only know of the Hadith of Abu Umamah, like this, from this route. Some of the people of knowledge have criticized 'Ali bin Yazid (one of the narrators) and graded him weak, and he is from Ash-Sham.

Jami` at-Tirmidhi Book 14, Hadith 84