Does electron's magnetic spin mean that we can think of it as having the two magnetic poles?
Yes. There are no known magnetic monopoles, see: Magnetic Monopoles
Does the spin mean that it generates magnetic field even if it is at rest?
Yes, but as regards "at rest", you should read this answer: Electron at rest
Magnetic spin isn't really a proper term, but an electron's spin is directly linked to its magnetic field, if we were to say that only moving electric charges produce magnetic fields, we would have trouble explaining how a static magnetic "works".
I would also stress that spin in this case is purely a mathematical idea, an electron does not resemble a very small rotating football in this case, its a bad choice of words made years ago.
If you read the links, you will get a better answer than this short reply.