I think it would be fine to put it on the concrete slab, and it would be fine to use scrap wood, as long as it isn't treated. We have huge brush piles all over our property, and there's no particular structure to them. That's what makes them great for small animals and birds.....there are tons of nooks and crannies in them.
Your brush pile sounds great. Good luck with it.

One advantage to putting a brushpile on a concrete slab is that as the wood decomposes you must add additional material every year. After a while it is good to rebuild the brushpile. You will find that in several years a nice layer of compost has accumulated that you can use for many things.

No problem. I'd throw a few shovelfuls of dirt over the concrete. But then, I build brush piles for my quail and they like to scratch around.

You can build a loose sort of framework with the lumber, but you will need cut branches with leaves to make it look homey.

If you want birds instead of mice, make the interior pretty loose and airy. Just tight enough so the smaller predators (cats)can't get in.

I've got shallow pans of water inside the edge of my brush piles so the quail can drink without being exposed. That helps to keep the water cooler in the summer.

If you make the pile taller, the tweeties will move into the top part of it and stand around on the top branches, twittering away.