If you have rust on your car take it straight to dealer. This "should" (I use inverted commas there as the dealer will no doubt try and get out of it) be covered under your silly long paint warranty (12 years I think it is off the top of my head).
As for the white worm on the badge, that's a common fault on the MK5 and will need to be replaced by yourself. As for getting it off these posts from Steathwolf and Hurdy will assist you:
Depends on which badge version it is. The earlier ones were basically metal badge with black paint. The later ones were black base with a separate silver VW emblem could be removed. If it's the former, you need to buy a new badge+mechanism. If it's the latter, a screwdriver or similar can be used to prise off the metal VW emblem.
The rear one needs a little persuasion to come off as it is held on by several clips. Use something like a cradit card to get under the badge and once under lever it off gently and follow the badge around the edges, levering as you go. It should pop off easily. 
Your looking at about £90 for a new one from the dealer so unfortunately not cheap.
