Hello
You'll have to post some pics of your lovely furbaby
In my opinion it sounds to me that your dog doesn't view you as pack leader and you need to get this with him which means going back to basics....I would walk him on a halti/gentle leader/head collar, this would give you complete control over him, it would reduce pulling etc then you need to master the walk itself. When we got Diesel we took him to see a trainer who helped show us how to walk with control, if you read "Pulling when walking" thread this will help you.
Secondly have you thought about getting a long lead or tracking lead? this will help you to reinforce the "come" command....ie, let him move away from you (not too far at first) say come and pull the lead to bring him to you & when he reaches you use his favorite toy (if treats don't work) to play with him for doing as you ask. I was told too by Wildmoor not to use the same toy he has in the house it's got to be a toy he only gets outside for play like this, I wouldn't give him free run off lead if he won't come back. You also need to teach and reinforce the "leave" command for the squirrel issue, start by doing this with his fav toy, leave it in front of him and tell him to leave every time he leaves by looking away from it he gets it and you play with him, this will then make him realise what leave means. You can then take this outside say the word and when he looks away he gets to play with his toy - it's all about having fun!!
Also I would stop making a big thing about putting his lead on him to go out, this only excites them and then they can pee...you need to control even this part of the walk. I would get him to sit calmly before even getting the lead out, you need to keep calm and don't talk to him as this will excite him. Then once the leads on walk him calmly to the door, every time he pulls or gets excited get him to sit and be calm, only move forward when he's calm....this may take a while to get out of the door but if you persist he will soon realise that he gets nowhere if he's excited. This should also help with the pulling too and the squirrel chasing.
As for the barking we taught Diesel the "quiet" command, but this was taught to us by a professional, using water in his face (he's not scared of water at all now because of this and in fact loves it so it didn't harm him)....we only did this twice before he realised quiet meant quiet so I would recommend maybe seeking help before going ahead with this...some may think a noise distraction would be a good idea but again I would seek help before doing this unless someone on here can advise the best way.
I hope some of these things will help and I'm sure there'll be others on here with their views on how to deal with these issues.....good luck and keep me posted with your progress
Lynn
x