First things first, after your dog mauled him did you take him to see an avian vet? Birds have hollow bones and they are very fragile, also such a mauling may have caused internal injuries and birds will hide illness and injury as long as possible so he could still be having problems from this incident which is why I am asking this.
Next thing is his cage. If his cage is small enough for you to hang or be knocked over by a terrier then there is a very good chance that it is way too small for him. With that said could you let us know the measurements of his cage? Length, width and height. Pictures would also be helpful.
I would remove the mirror. Does he have any other toys? How many people are you speaking of when you say we all try talking with him? Based on the contents of your post, I am thinking that this is your first bird and also that you have very limited knowledge of parrots, is this correct?
These are my main questions after going through your post, at least for now. There may be more even in this reply as we go along. For now I am going to reply as if you know nothing at all.
At 10 yrs. old Billie has indeed had it rough, but if you take it slow there is no reason that he can't get through this and be the truly awesome creature that he really is. At this point he has no reason to trust any human, but if you are patient you can earn his trust, but it is going to take some time and there is no way that I or anyone else can tell you how long it will take. Now as I keep referring back to your post I see that nowhere does it tell me how long you have had Billie so could you tell me how long you have had him? And since I am still asking questions here are a few more. What are you feeding Billie? What time does he get up and go to sleep? I know that this is a lot of questions, but everyone of them has a direct bearing on his health and on his present behavior.
For now, the best way to approach this is to limit Billie's exposure to people to two or perhaps three people, these being the ones who will be the ones who take care of him. I am assuming that he is an only bird, so if his cage can be placed so that he can see you a lot, but is also out of the way so he doesn't have to deal with everyone, it will help him to adjust and let him know that he is not all alone. He is a flock animal and although he has some people issues to work through, he also needs to feel that he is a part of what is going on. At this time these two things are in conflict and it can be a little touchy balancing them for the best results. You will need to set aside 2 or 3, 15 minute periods of time each day for him. These times will be for you to talk to him and to carefully observe him as well. You have the right idea, in that talking to him is going to be your best method of reaching through all that has occurred to him to gain his trust. To start with this you will need to observe him from the time that you enter the space that he is in. Then you will start to approach him and as soon as he starts to get nervous or what appears to be excited and either moves away from your position or starts to run about, stop and do not approach any closer for the remainder of this session. Every session begins in exactly this way. then you talk to him in a calm voice, including in your dialog words and phrases of praise telling him how good he is and that everything is alright, perhaps you can even make up little ditties that you can sing to him. The remainder of what you actually say doesn't really matter at this point but I find that it is easier to tell them how much I care about them and tell them all about my hopes for their relationship with me and things that I would like to do with them. These are things that I talk to mine about. When the time is up say good bye and leave. If you do this after a period of time you will find yourself at the front of his cage. It is during this phase that you will be able to introduce treats into the equation. You will continue to do exactly the same thing as I have already described but you will offer two or three treats during your talks. I would start with, perhaps, thin slice of apple with no seeds in it, the seeds are bad for them. You can use a different treat if you want to just make it long enough that he does not need to touch you in order to get the treat. If he does not take the treat, that is fine just put it where he can still get to it when he is ready. continue these talks in this manner until he is taking the treats from you on a steady basis. Then you start reducing the size of the treat until he is taking a treat from your fingers without biting at you. This marks the point where you are finally starting to earn his trust. You still have a ways to go , but it is the start. Once this is done and he is taking treats from your fingers without biting on a regular basis then you proceed to the next step. This is where you position yourself directly in front of his cage and open the door for your talks. Again you proceed as before but now you are offering him the treats directly from your fingers without the cage bars between you and Billie. If all goes well he will take the treats from you without biting and if so then you place your hand so that your fingers are inside of the cage without disturbing him and then your whole hand. All of this time you are building his trust as well as your own in him, this is all very important for both of you. The next step will be when you start offering him treats held in such a manner that he must step up on your hand to get the treat. He must step on to your hand totally of his own free will. When he does this on a regular basis then you will be ready to start him on target training, which we can go into when he is ready for that.
Now, if you can bear with me a little longer, I think that a little information about Senegals might be helpful to you. To start with they are very intelligent, and in some ways are like having a child of 3 or 4 yrs. that just doesn't ever grow up. They have a tendency to choose one person as their special friend and at his age he will think of this person as his mate. He doesn't think of himself as being human, nor does he think that this person is a parrot, but he does expect that his human will at least try to act like a self respecting parrot should act, and he will let you know if you are not. Once he has chosen and bonded with this person, he is jealous of other people taking to much of this persons time. time that in his mind should be spent with him. He is loyal to this person and will do his best to protect this person from anything that he perceives as a threat. This protection can range from nips meant to guide the person away from the threat all the way to taking matters into his own hands and attacking the threat in an attempt to drive it away from his person. you must never try to punish him for these actions as he is not misbehaving, he is only doing as his nature dictates that he do to protect his family.
Please read this link, I think that you might appreciate it.
http://www.african-grey-parrot.com/A-Pa ... ights.aspx