My basement kitchen has this circuit (20AMPs or 40AMPS-not sure) , can I run power tools on it?
What you're looking at is a 40A circuit at 240V.

It's possible to split a 240V circuit into dual 120V circuits, but then, it's the amperage on the breaker -- i.e. this splits into two 40A circuits, not into two 20A.  

So a 40A breaker is absolutely useless for creating 20A circuits. 

If you want 20A circuits, the breaker must be 20A.  

This 40A breaker is certainly for an electric range.  Another problem you have is that electric ranges of this era were wired without a ground wire.  Trying to run equipment in a garage without a ground wire would be nuts.   It would take a great deal of re-work to try to turn this wiring into a usable circuit that could feed a subpanel, or be down-breakered to directly serve 20A circuits.  The breakers are cheap enough; it's the cost of retrofitting a ground. 

However, a kitchen will certainly have ordinary kitchen countertop receptacles. It's supposed to have two 20A circuits. That should be plenty for saw and dust collector.  

And you are correct, saw + dust collector on the same circuit is not likely to work.