Welcome, twice (or is that four times?) bitten. You say this yorkie is 4 years old and has lived with you for a year and a half. Is he a rescue? If so, do you know his history?
Also, what size is he? Smaller yorkies tend to exhibit more fearful behavior. From what you've said so far, I don't think he's angry -- I think he's scared, and experience has taught him that biting tends to make scary things (strangers and hands) go away. Inappropriate behavior, but effective.
The potty training is a whole 'nother issue, with literally hundreds of topics if you look in the training section.
Biting is serious behavior, and once a dog has shown such willingness to bite, he can never really be trusted again. Make sure you keep him away from children.
I'd suggest that for such a wide range of behavior, you hire a trainer. Hire someone who uses POSITIVE techniques, and try to find someone who has experience with small dogs. My guess is that they will recommend you neuter him. This should help with the house training and the aggression. However, with the wide range of problems you describe, you probably want a professional assessment. Hope this helps.
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