Puppies are going to chew no matter what...you have to puppy proof your house just like child proofing its for there safety...put all your shoes, hand bags in a closet...buy your baby some chewies for her to chew...if you catch her chewing on something she is not suppose to say NO take it away and give her a chewie and say good girl...if you yell no to her in a loud voice, she might take it as attention good or bad and will never stop cause she wants that attention.
and the kittie chasing I would try something like the "leave it" command.
and the door thing same thing use the "stay" command...you will have to work with her on these commands daily, it will take sometime but the end results are worth it....use treats while training...when she does what you want her to do tell her she is a good girl and pet her and give her a treat....she will than learn that if she "stays" or if she "leave it" she will be making you happy and gets a reward and thats all our babies want is to make us happy...Good luck