I cannot access the first partition (here F:) after I formatted that system partition with MyDefrag.
"Formatting" and "defragmenting" are totally different operations. You cannot format a volume with MyDefrag.
Why can't you access f:? Can't you see the volume? Is there an error message?
ps: What do you mean by "privileges"?
You need certain privileges to access data. When running MyDefrag for example you'll get a dialog asking you to give MyDefrag admin privileges (if not, you've disabled UAC). When Window applied that "fix", it's possible that it has removed "you" from the users that are allowed to access that volume. That would explain why you can still access the volume under Linux (Linux gives a dawn about NFTS user rights).