Hi,
Your dog should take to rats naturally, try and start her off easily, not thrown in a confined space as she will get bitten and this could put her off for a long time , if you know someone who has permission on rats see if you can go along and let your terrier know what it's all about.
With regards to the selective deafness, you should have really got this training done at an early age, although terriers by nature are strong willed. your problems should ease with some regular basic training.
Best of luck.
ps, get your dog chipped if it's not already