1)
Verse 20 said that only Yehudah was with Beis David. Why would Binyamin help Rechav'am?
1.
Refer to 11:13:1:1.
2)
Why did they expect to be able to defeat 10 Shevatim?
1.
Malbim: They thought that Hashem will help them, since kingship was promised to the seed of Beis David. This is why it says "li'Rchav'am ben Shlomo."