How should I understand this rule (rulebook p.41, Hunt Re-rolls)? Does it refer to the last known position of the Fellowship, or does the free peoples' player have to tell the shadow player that he now got X re-rolls which would help him to determine the current position?
According to the 2nd Edition rules (although the 1st Edition rules do not differ in this respect, although it clarifies it in a different way), when determining the location of the Fellowship, the Frodo & Sam figurine's location is used. This may be the current location of the Fellowship, if the Fellowship is declared or revealed. Otherwise, it will be the last known position (LKP) of the Fellowship and the Fellowship Progress Counter will indicate how far the Fellowship has traveled from that last know position. Since the LKP of the Fellowship is always used for all rules, including Hunt re-rolls (Hunt Re-rolls use the position of the Ring-bearers figure, not the current position of the Fellowship), no extra information is revealed to the shadow player.
The 1st Edition just flat out tells you to use the Fellowships last known position.
My copy of the WotR rules don't have a page 41, but on page 19 of my rule book, the following text occurs:
"If, during the Hunt, the last known position of the Fellowship" [emphasis mine]
Think of it as the Shadow following the trail of the Fellowship. Getting out from under a Nazgûl is in fact one of the motives to declare the position of the Fellowship.
What's fun is that the Free Peoples player doesn't actually know where the Fellowship is, either. They don't have an actual position until they are declared, so any rule that acts to give clues about what that actual position might be wouldn't work anyway.