Are they open year round? I was wanting to go in December as part of my road trip

Yes, except for major holidays. Everything other than camping closes at sunset. I recommend hiking the Charon's Garden Wilderness trail if you are stopping by the Refuge!

Yes. At least see crab size if you're going to Charon's Garden or climb Elk Mountain. You can drive up Mount Scott. It's okay in a touristy way.

I love the Lost Lake trail. I saw no wildlife when I was there but it is beautiful and quiet.

Charons garden is great, but you will see a lot more wildlife on the bison trail if that's what your looking for.