The two chicken-related incidents sound a lot like resource guarding. It's a perfectly rational behaviour in many ways - if someone tried to take something from you that you regarded as valuable - be it a nice slice of cake or your mobile phone, you'd be doing something about it too. This is likely to be heightened in a dog that has been previously left seriously hungry, and so will attach more value to food. Obviously, however, it's an undesirable behaviour.
To manage the behaviour, I'd be putting the dog's food in the bowl and then leaving well alone until the dog has finished eating and has gone off to do something else. If chicken falls on the floor, leave it, the dog will find it anyway!
The standard advice for preventing resource guarding from becoming an issue would be to add more food to the dog's bowl whenever you approach it, so that the dog sees your approach as being a good thing. However, that may be bit high risk for a dog that already has issues around food.
The other time he tried to bite me was when I went too close to my dad and nudged his arm (I think the dog thought I was going to hit my dad)
He immediately realised he had done wrong.
Went over to my dad and started trying to lick him and sat next to him.
So it sounds as if the dog thought there was going to be aggression (perhaps he's witnessed domestic violence in the past?) and got a bit confused. He did, however, stop himself from actually biting (no real pressure applied?) and then realised his error.
It's harder to know what to do about this one, but I would take comfort from the fact that the dog didn't properly bite, realised his error and then displayed some bonding type behaviours. It may just be part of the healing process your dog is going through, finally realising he's safe now.
I agree with others that you'd benefit from a session with a behaviourist - look for someone CCAB or APBC accredited. You'll need a referral via your vet, which is normal, as they have to rule out physical causes first (e.g. pain is a common cause of grumpy, snappy dogs).