I have 2 chihuahuas (soon to be 3!) and they usually start weezing when they get excited or on their leash.. i have never met a chihuahua that hasn't so Im pretty sure its normal for them. And about the training.. i trained my own chihuahuas a few tricks like sit, lay, jump, beg,and go to the couch (they have there own miniature couch ). It took a while to train them becaue all they could think about was getting there treat!