No - the two are not related. Woody Allen was born Allen Stewart Konigsberg. Tim Allen was born Timothy Allen Dick. They both picked up their shared surname when they adopted it as part of their stage name.
Apparently not. Jeff Allen was born in Saulk Village, Illinois in 1956.* There is no record available to indicate Tim Allen ever resided there at that time. *Source: http://premierespeakers.com/jeff_allen/bio