Can you get head lice from walking in the woods? I noticed a tiny brown bug crawling on my phone and didn't know if it fell off my head

No. Head lice are specific to humans, and cannot live off the scalp. Unless you were butting heads with someone in the woods or sharing their cap/comb etc, that was not lice. There are countless insects it could have been, but if it was on your phone, then it's no longer on your scalp. Remember to always check for ticks after being in the woods - if you get them off in time, they can't spread disease.
Highly unlikely. Head lice live on people's (usually kids') heads, they don't wander around homeless in the forest, so your bug is not a head louse. However, every wooded area has literally hundreds of species of "brown bugs" living in it. If you really want to know what it is, put it in a bottle or baggie and bring it to a doctor or insect expert.
Q 4 Wilderness, Derm. I referred this to specialists in wilderness medicine and dermatology. Let's see what they say about this bug and the need to comb or take other steps on leaving the wilds of wi.