As many of you know, my 6 month Husky, Royce, is quite a handful. Thankfully, with his training, he's slowly getting better. He's probably 95-99% potty trained, he goes to sleep around 8:30ish and usually wakes up around 4ish, until he gets his food, then he goes back to sleep until my wife and I both wake up. But, there are two problems that constantly seem to happen. One is something that's happening practically everyday and the other is a future concern.

First- Royce is a biter. It's mainly a playful bite. He will put his mouth around my (and practically everyone else he comes in contact with) arm and hands and will slightly chomp down, but he usually lets go. But when he doesn't, we grab the inside of his mouth and pinch down, telling him "NO," because that was a tactic that worked on our other dog, as she stopped biting after about a week or so. But with Royce, it seems as though he thinks we're continually playing a game with him, and once we let go, he goes for the hand again. The entire time he's awake, he's chewing on something; whether it be his toys or something he found laying around the house, he's even begun gnawing on the furniture Anyways, the main reason why I'm posting this, is because earlier today, my wife's grandma was in town and he chomped down on her hand, harder than he usually does. He wouldn't let go, until I literally had to pry his mouth open. She wasn't badly hurt, but it left a pretty deep mark.
I'm concerned and I really don't know how to break this habit. I've been told that this is just a puppy thing, and his biting and chewing everything will eventually pass. I've also been told this is something I need to jump on immediately and it might even be better to buy a muzzle. I really don't wanna do that, but I'm running out of options. Has anyone else had this problem? Is there a better solution?

Second- With Christmas coming up soon, I'm extremely concerned with taking Royce home to Michigan, from Chicago. He's never been in another house, besides ours and he's also never seen, or played with a bigger dog than him, which there are about 3 in our family. I guess what I'm mainly concerned about is since everything will be brand new smells to him, he'll go to the bathroom all over my parents house, aunts house, or pretty much any place we'll take him. I know it's something he needs to do, so he'll be used to it eventually, but is there a way to feel better about it, or should I just roll with the punches?

There are a lot of threads about what others have done with puppy biting. I've commented in quite a few of them, but I'll quickly revise. I'm an advocate for a physical correction, ending play completely and removing myself immediately after the correction. I grasped his muzzle shut gently, made him sit, stared at him directly in the eyes (most important part IMO), and said in a low growly voice "No", I stared at him till he stopped wiggling and "submitted" to my grasp, them left the room. Worked fast and was effective. Some people don't like to give physical corrections, but sometimes it's what they need for them to realize that it is an unacceptable behavior and they don't get to have fun anymore. If they keep getting away with it or if the correction and punishment aren't strict enough, they will keep doing the behavior. You have to make it an unpleasant experience, that way if the opportunity arises to do that behavior again, they chose to not do it because the correction and punishment are not worth doing said behavior.

When Biko (age 3) gets carried away with biting I pinch him just behind the rib cage. In a short time he learned not to get carried away with biting. The harder he bites the firmer the pinch I think he just got tired of wondering why I was pinching and stopped biting. With my experience he'll out grow the biting you just need to hope you still have an arm. The only time Adobo (age 6) might munch my arm now is if she gets overly excited about going for a ride or walk.

As to the marking take him to a Petco or Petsmart and see how if he controls himself.

It's been a day so far and I've been grabbing his muzzle whenever he bites down on our hands and/or the other dog. I hold it until he stops trying to get out of my grasp and then I let go. Both times that I've done that, he hasn't tried to snap back, but after a few minutes, he'll try to bite again. I know this is a process that will take some time, but I'm happy that it seems to have an effect on him. Hopefully I can have him stop, before we take him to the big family gatherings for Christmas, which seems to be my biggest concern.
We took him to a dog park for the first time ever and he was terrorizing the little dogs, but was terrified of the bigger dogs. Again, I know this is something he needs to get used to, but I hope that he'll start to mature soon, as he's been (and I'm trying to say this in the nicest way possible) a nightmare these past few weeks.

Since you are starting a new training method, he's gonna test you to see if you truly do mean business. Once he understands that it isn't fun to be overly mouthy, he'll stop

How long did it take Kale to stop her biting? It seems like one day, he'll listen and stop, then the next day, he'll go back to biting.

A few weeks. It's definetley not a quick fix. Stay consistent and strong; just like with human kids, the moment you show weakness, it'll start all over again. I should know, I was a horrible teenager! Hahaha