I'll answer the first three questions only leaving the last for another post.
Basics Although it is patented in US, is it "working" worldwide?
It is common for a patent to be simultaneously obtained in every country that is a party to the international treaty governing patent filings. But, this isn't done for every patent. Without checking you can't know.
two countries have the same patent from different inventors? When
someone brings patent to patent service in his country, the patent
service will check if there same patent anywhere in the world?
One can imagine from pretty technically obscure ways that this could happen, due to inconsistencies between national laws that are changed at different times to convert to the first to file system, regarding first to file systems v. first to invent systems (to oversimplify).
But, usually, the existence of a patent anywhere in the world will be "prior art" that defeats a later obtained patent anywhere in the world and would result in the summary defeat of an infringement case brought by the later patent.
Basics If last sentence is false, - if someone from country A stole
patent from country B, then inventor from country B should go to
country A court?
Normally, the investor from country B and that inventor's licensees would gather up a file showing that his patent was prior art before it was applied for in country A, and then use this only upon receiving a cease and desist letter or being sued for infringement in country A.
Some countries allow patents that have been issued to be invalidated after they have been issued in the absence of litigation (including the U.S. in the inter partes review review process in some cases). But, usually, having a case lined up to swiftly and cleanly defeat an infringement claim if made would be enough.
How (US) law describes expiration of patent? What does it mean? Can it
be repatented? Can anyone free use expired patent?
Generally speaking, when a patent expires, the patent enters the public domain and anyone can use it for free.
Patents on certain medical products can be extended for up to five years if there have been delays in obtaining FDA approval that reduced the available marketing time for the product to less than fourteen years.
CAVEAT: There are a handful of countries that "just weird" and don't follow the general rules that most countries of the world have agreed to by treaty. Cf. these countries with anomalous copyright laws.