What did Sha'ul dissect the cattle into pieces?
Malbim: He showed that just like a life is possible only when a being's limbs are intact and connected, so Ru'ach of Gevurah and civil life are possible only when man is connected to his fellow man to help him from any afflicter. Therefore it says that they went like one man - that each limb feels the pain of the entire body.
Why did he say "v'Achar Shmuel"?
Radak: Not everyone had accepted Sha'ul as king. One who does not want to go after me, he will go after Shmuel. This way, all will be zealous to go.
What is the meaning of "li'Vkaro"?
Rashi: It is 'to his animals.'
Sha'ul sent to "all the borders in Yisrael." Would people at the borders hear and be able to come within seven days? Rashi (Bamidbar 13:25) writes that it takes 40 days to walk from one end of Eretz Yisrael to the other!
Refer to Bamidbar 13:25:151:1,3,4 and the notes there.
Perhaps indeed, the Sheluchim could not reach everyone. Only 30,000 men came from Yehudah, even though Sha'ul threatened to break the animals of one who will not come. 1 Asa had 380,000 soldiers from Yehudah, at most 15 years into his reign (Divrei ha'Yamim 2 14:7, 2:15:10,11). He became king only 100 years after Sha'ul! (PF)
We do not find that he went to do so. It seems that everyone who heard, he came. However, perhaps some did not, and he pardoned them, just like he did not kill the ones who had disgraced him (verse 13. - PF)