Update*

I have to apologize to Dekel that I've taken so long to post this update. He answered me a while ago with my questions on the Israeli government. Here is how he explained it:
"In Israel, the democracy is a Parliament democracy. That means that the people choose the Parliament members, and the member who has the highest chance to form a coalition (usually it's the party leader with the most seats)gets the chance to form a coalition.
In the last elections, Netanyahu got one seat less the Livni, the main opponent, but most of the parties of the Parliament wanted Netanyahu as a PM."
I still want to know more about the opposition situation. I'll be looking more into that in the future.