I have a male husky, Nova, coming up on two years here in a few months.
He's pretty stubborn. I understand that he'll get bored on a rainy day, but he does these things even after long walks or playing at the dog park. When he wants our attention (usually when we're preoccupied with something or eating especially!), he'll mouth our hands or try to push up our arms, and if those aren't available to him, he kind of does a head butt with his mouth, accompanied by a short bark or grumble. And he'll kind of nibble with his front teeth, which can pinch me sometimes.
I'm not sure what to do to fix this, and he does it fairly often.
Right now I tell him to stop or go lie down, which of course he ignores even though I KNOW he knows what it means. And if he still does it, then we count to three. It usually goes, one...continues, two...pauses for a second and then pushes his head forward with a bark and foot stomp, three...he darts away to him room (timeout).
So, he knows the consequences, he just doesn't care I guess?
Half the time I'm holding back a laugh because his attitude is so ridiculous, but then sometimes I'm annoyed because I need to be doing something or I'm eating and I don't want him begging (If I've ever given him people food, it's outside of us eating).
I've also tried ignoring him when he does the little head butt thing, but he kept doing it so much that it really pinched my leg and gave me little bruises. He's persistent.
So any other advice for this? I've considered getting a beep/buzz collar to address the whole not wanting to come inside when I call thing as well.

I should add that another stage in this, is him jumping up with his front paws.

And it just happened again, while I was playing with him!

We were playing tug and toss with one of his toys, and after I threw it for like.. the 5th time (which usually he'll play fetch for awhile) he just left it. I went to grab a drink and came back to play, and he started to look like he was going to be stubborn, so I said, "go get a toy." And he also knows what this means.

Apparently he didn't want this, he didn't want to go play outside (it's rainy), so he started his little spiel again. 1-continues, 2- he jumped up and stomped/barked, 3- scurries off to his room. I don't get it, and I'm not quite sure what he wants. He has toys and bones to occupy him on rainy days, but only chooses select times to play with/chew on them.

This sounds a lot like Ami when he does not have enough exercise - even when he does 5 miles a day.  The only time he has enough is when he spends the afternoon with his buddy, Archer.

Also, sounds like you enjoy your imp-  he probably picks up on that

This all sounds like normal husky behavior, especially for one coming up on two years. Personally I always have liked the quirky antics of the breed. An old saying on this site is "a tired husky is a happy husky". Extend your walks some if you can and keep it structured, have him walk at heal and mix it up a bit to keep his mind working. Try teaching gee and ha (right and left) as you walk this can help if you decide to scooter, ski, bike, or run with him (huskys shine when you work them like this).
Rainy days can still be a good thing if you can find a large store that will allow dogs inside(we have a lowes that allows dogs). I like stores because my dog is working body and brain, lot's of stimulus for the brain and lots of walking room for the body, but please make sure your dog can behave in the store, it would not take much to loose the privilege.
This is just a few things, I'll bet others will have more to add, and best of luck.

It was finally nice today, so he got nice and tired at the park. We'll see how long this lasts
I don't really have him walk at my heel.. I tried to teach him awhile back but I just kind of let him smell things. He tends to pull when he's excited, but otherwise he does pretty well. I think i should try to get back into the structured walks, though. So generally, since he's about 5 feet away, I say, "This way," to get his attention to turn.

I've taken him to petco several times, and he does ok, but also can get excited, as he LOVES people. But once we get going through the aisles, he just kind of looks around.
He tried taking a hoof off the shelf once, but it sprung back since it was attached and kind of spooked him

I'd also like to bike with him, but I'll have to read on that. Right now my husband jogs with him at night (not too long, a mile or less probably).

And he probably does notice my amusement most times. I really try to hide it because it isn't desirable behavior, but I'm sure I have a terrible poker face.

So I guess in the meantime, timeouts are ok?