What American government position would the President of Israel most correspond to?

Factual Questions
1

I’ve never taken a political science course and I’ve tried to educate myself on world governments, but some are just more difficult to understand than others. So, the Prime Minister of Israel is the real power in the country and the president is more ceremonial, but… he has the power to appoint certain officials and to appoint (or at least nominate) a new prime minister if the serving one becomes incapacitated (as happened with Sharon’s massive stroke last year), so he’s really not powerless after all, but is controlled by the Knesset.

What, if any, position in the U.S. is this similar to? VP? Or a key Senate position?

Can a president nominate himself (or herself) to be PM?

Thanks for any comments.

2

Many countries have two leaders: the Head of State and the Head of Government. The Head of Government is the one in charge, while the Head of State is confined to ceremonial duties and a few odd powers.

In the UK, the Queen is the Head of State and the Prime Minister is the Head of Government. That seems to be the situation in Israel: the President is Head of State and the Prime Minister is Head of Government.

In the US, the president is both head of state and head of government (It’s the same in France IIRC). Thus the US president has the duties of both the Israeli President and Prime Minister. There’s really no one who would have the Head of State powers in the US.