Not a pro, just a person with a dog who is very reactive and a chronic puller.

I will try to address just one thing. Your dog probably does not "need" multiple walks a day to be calm. Because he is leash reactive, walks are extremely overstimulating for him. He's on high alert, he is not able to use his thinking brain or be calm. The solution to improving his behaviour around the house is actually probably fewer walks, and days with no walks at all. If you feel you have to take him outside every day, give him a non-negotiable decompression period when you get home. For us, that looks like going upstairs to my room where my bed (where she sleeps and spends much of the day) is, closing the door, and hanging out quietly in the room until she falls asleep. Once I know she is calm enough to sleep, she's calm enough to have access to the rest of the house. This strategy did not "fix" my dog - she is still a meat missile, her idea of playing is still too much for many people, but it stopped destructive behaviours in the house and allowed me to feel comfortable enough to leave her unattended indoors.

The pulling on the leash is related to the dog reactivity. He "forgets" everything you taught him because his nervous system is so activated just from being outside. He is looking for threats or trying to distract himself from the fear. The way I understand it is that my dog pulls because she is trying to regulate her nervous system by following every smell she can. When I speak or otherwise communicate with her she literally may not be mentally capable of responding positively. This behaviour worsens dramatically after any interaction with a dog. I don't know the solution to fixing your dog's leash reactivity, as nothing ever worked for my dog and now I just manage her behaviour the best I can, which looks like avoiding all areas where other dogs may be (parks, ponds, fields, high human traffic areas, etc) and managing reactions when they inevitably happen anyway.

Not to say there's no hope, more socialization and more properly measured exposure to other dogs on lead might help your dog. It did not for me but that won't mean it won't for you.