The deer, why voldemort can't straight up murder harry, and that old lady are all explained.
The deer and voldemort parts would be spoilers but I can tell you about the old lady
old lady was killed and then turned into a puppet by voldemort as a potential trap for harry if he went there for clues. she didn't say anything in front of hermione because she was actually voldemort's monster snake in disguise. harry can actually talk to snakes since one of his ancient ancestors is some other guy that's considered a bad dude in harry potterland. if the old lady tried talking in front of hermione then she would've known it was a trap
the deer is interesting and gets revealed in the 2nd part of DH.
And as far as them always getting away, that stuff always seems more plausible in the books. Take LOTR for example. Reading that it seems to make sense how sam and frodo make it to the end. In the movie it seems like they're just lucky or all the enemies are retarded