How do I search for FB users who worked in a certain company (e.g. Microsoft)
How do I search for FB users who studied in a certain school (e.g. Standford University)
What query should I use to fetch the above information?
You can't.
Work and education history require specific permissions in order to get them for a specific users. Facebook wouldn't give it to you any other way, it's private information.
Generally you can only search by name in the Graph API, not by properties.