Once grains have been crushed, how long do they last?

I got some crushed grains for what was going to be my first AG brew. But I decided to try something easier first, so I can test things out and be ready to drink it within a few weeks.

So looks like I've got ~12 lbs. of crushed grains that I'll be holding on to for minimum of a week, possibly 2 before I can do another batch.

Is this bad? Is there anything I can do to maximize freshness?

Keep them in a cool dry place to maximize freshness. They will be fine for several weeks as long as they are in a sealed bag.

Would it be good to stick them in a sealed bag in the refrigerator? Or is that frowned upon? Better to just put it in a closet?

Yes, you can freeze your grain. I do it all the time

What is the thawing process like if you freeze them?

I often wait weeks or months. As long as a grain stays dry (store in low humidity) and cool it can last for a year or so, even when coarse-ground like the grains in the baking section of your grocery store. They go bad only through attack by fungi, insects, and bacteria, all of which require moisture.