1. Take baby steps with the leash. Whatever you do, never make it seem like something scary. It may just be that they are small, you are big, and when you reach down to leash her, she gets scared of the huge monster reaching towards her Another technique for leash training puppies is the one where you leave the leash on for a little while each day and let them drag it around for a while. If she is really afraid of the leash itself, you may have to just lay it on the floor with her and let her come to it and convince herself that it's not dangerous.

2. Just make sure not to make a fuss if you catch the pup 'in the act' when it's in the house. If they learn that they will be punished when they are caught going in the house, they may learn to be sneaky and hide from you to avoid being caught (one of mine was like this when we adopted her). Just be patient, clean up the mess and take her out regularly (like every hour at first). Dogs naturally want a clean 'nest', so just work with that behavior.