What are the Ayarim on which they rode?
Rashi citing Targum Yonasan: They are young horses.
Radak #1: They are young donkeys, like "Osri la'Gefen Iro" (Bereishis 49:11) and "Ayir Ben Asonos" (Zecharyah 9:9). Perhaps they are the best for riding in those lands.
Radak #2: Perhaps mules [born] from horses [and donkeys] awe called Ayar. We find that Ayar is not limited to donkeys - "v'Ayir Pere Adam Yivaled" (Iyov 11:12). Perhaps this is because Pere is a wild donkey.
What are the Ayarim that they owned?
Rashi: They are cities without a wall. Radak - the verse used the same word as before (for animals) for a pleasant expression. (Normally, they are called Arim.)
Are Ya'ir and Chavos Ya'ir the same as Ya'ir ben Menasheh and Chavos Ya'ir mentioned in the Torah (Bamidbar 32:41)?
Radak: This would be astounding. If so, Ya'ir was more than 300 years old 1 ! We can say that it is a different Ya'ir 2 , and Chavos Ya'ir are not the same cities. 3
Abarvenel: This was Ya'ir ben ha'Gil'adi; he is not Ya'ir ben Menasheh. However, we can say that they are the same Chavos Ya'ir; it does not say that Ya'ir ha'Gil'adi conquered them.
Metzudas David (Divrei ha'Yamim 1 2:23): Ya'ir ben Seguv (1:2:22) is not Ya'ir ben Menasheh. He called his cities Chavos Ya'ir, because he had the same name as Ya'ir ben Menasheh, and also many cities. Ya'ir ha'Gil'adi called his cities Chavos Ya'ir for the same reasons.
Yalkut Shimoni (Shoftim 3, 42) says that Ya'ir ha'Gil'adi from Chavos Ya'ir was from Shevet Menasheh. If the source to say so is the name 'ha'Gil'adi', why did he add 'from Chavos Ya'ir'? It seems that he holds that he is the same Ya'ir who conquered Chavos Ya'ir, which were in Menasheh's portion. However, it could be another support that he was from Menasheh, for he lived in Menasheh's portion (if they are the same Chavos Ya'ir. - PF)
Yiftach's reign (the six years after Ya'ir died) was 340 years after Yetzi'as Egypt. However, Ibn Ezra (Bamidbar 32:41) learns from Divrei ha'Yamim 1 2:21, 22 that Ya'ir 'ben Menasheh' was the grandson of Machir ben Menasheh's daughter. If so, perhaps he was born in the Midbar, after leaving Egypt. (PF)
Some say that Ya'ir ben Menasheh died in the battle against Ai. Refer to Yehoshua 7:5:2:2.
Malbim: They were Chavos ha'Gil'ad. He called them Chavos Ya'ir, for he had a semblance of the strength of Ya'ir ben Menasheh. Kara Es always refers to the actual name. Kara followed by the prefix Lamed (or here, Lahem Yikre'u) is a nickname.
Are Ya'ir and Chavos Ya'ir the same as Ya'ir ben Seguv mentioned in Divrei ha'Yamim (1:2:22,23)?
Metzudas David (Divrei ha'Yamim 1 2:23): They are not the same. Ya'ir ben Seguv (in Divrei ha'Yamim) called his cities Chavos Ya'ir, because he had the same name as Ya'ir ben Menasheh, and also many cities. Ya'ir ha'Gil'adi called his cities Chavos Ya'ir for the same reasons.
Why does the Navi teach about their animals and cities?
Radak: This is why Ya'ir was a Shofet, because he had much wealth, sons and honor.