1)
Why did they want to kill the ones who said "Sha'ul Yimloch Aleinu"?
1.
Rashi: They had said so disgracefully, in astonishment. Malbim - this is like Mored b''Malchus (rebelling against the king).
2.
Radak citing Targum Yonasan: [They said] Sha'ul is not proper to rule over us.