Will this cabinet stay in place when I'm pulling tools out?

Yes — lock the casters before opening drawers. This prevents drift and keeps the cabinet stable under load.

Can I mount this against a wall or does it need to roll freely?

The locking wheels let you do both. Roll it into position, lock it, and it functions as a stationary storage unit. Release the locks when you need to reposition.

Are the drawers full-depth or do they stop partway out?

Drawer depth and roll-out range are not specified — test the fit of your deepest tools before fully loading. Most five-drawer cabinets pull out 75–90% of their depth.