I am restoring a 1970 Schwinn Suburban and I am at a loss when it comes to removing this bottom bracket. The crank arms do not come off normally (no way to use a crank puller) and they won’t unscrew. I have put some lube on the side opposite the drivetrain and maybe I need to wack it with a mallet but any advice would be greatly appreciated!!
This is what's called a 'one-piece' or 'Ashtabula' crank.
There is a nut you have removed (or that was already missing) on the threading. Then you remove the left cone via the slot in your second image. Sheldon explains better than I do: https://www.sheldonbrown.com/opc.html
Alan is correct.
Here's a diagram of this type of crank. Sheldon describes it with words but sometimes a picture helps.
The left side in the picture above is missing both the locknut and the lockwasher.
In an ideal situation you'd have a bottom bracket wrench for one piece cranks
If you are careful sometimes the adjusting cone can be removed with a screwdriver pushing on one of the slots.
The locknut and adjusting cone are left hand threaded.
Here's a Park video on this process.