1. How did Fred and George ever find out how the marauders map worked?? filch didnt know cuz he was a squib. and they wer wizards but snape was a wizard too and even he didnt know how the map worked.
A. Fred and George are clever Wizards, and took the time to experiment. Snape tried three times and then called for Lupin.
2. In the last book Harry enters the room of requirement from the hogs head. But in the sixth book, Draco Malfoy leads the death eaters inside the same room from Borgin and Burkes (remember he went to the shop to get the vanishing cabinet fixed). How come???
A. In HBP, the Vanishing Cabinet was located in the Room of Lost Things (part of the Room of Requirement), so that was where the Death Eaters appeared. In DH, a different version of the Room appeared, to suit the needs of the Resistance. When they needed food the Room produced the tunnel to the Hog's Head
3.If Dumbledore fought the battle against Grindelwald, how did he win it???? cuz Grindelwald possessed an "unbeatable" wand at the time didn't he???
A. You are putting too much stock into the "unbeatable" part of the the Wand. Since it had a long, bloody history, it stands to reason that, reputation aside, the Wand's owners do lose.
The original owner is said to have been murdered while passed out, Draco could disarm a weakened and poisoned Dumbledore,and Draco lost the wand be being physically disarmed by Harry. So, presumably, Dumbledore took advantage of some chance in the battle to disarm Grindelwald, winning the Wand.