Nick Petit

`chs("test")` isn't an expression, it's a string literal that happens to be wrapped in back ticks (special case), so deleteAllKeyframes() won't help here.
parm.revertToDefaults() should clear it (as long as the default isn't a channel reference wrapped in back ticks!) and parm.set() after that will behave as expected.

If that fails due to the default being for example `chs("test")`, you could try parm.setExpression("foo") followed by a parm.deleteAllKeyframes() followed by parm.set()...

No, you cannot apply DOF to the background plate LOP's background plate. The plate isn't projected onto the geometry and rendered, it is simply composited in as a background, in the viewport only (by default: Render Settings > Karma > Use Background > Auto) as a preview of what the final comp should look like.
Typically the background plate will already have DOF - the idea is to match up the CG camera to the physical camera the plate was shot with.
In your case, you'll want to first render the plate projected onto your BG geo, and then use that as the plate for the background plate LOP.

It's hard to tell without seeing the hip file unfortunately. If the car pieces fall apart right from the get-go, it means one of 3 things:

1. the constraints anchor names point to pieces that don't exist
   
2. the constraints break and disappear immediately upon impact with the ground
   
3. there are no constraints between the pieces that break apart
   

For 1) a hip file would really help to see what went wrong with the constraint creation.
For 2) the vehicle mass is too high or the constraint strengths are for too low and you have constraint breaking thresholds enabled for all constraints (including the soft constraints for metal parts of the car which shouldn't break) so the glue constraints break immediately, switching to the next constraints (soft with plasticity enabled) which then get deleted by the constraint breaking threshold as they probably stretch beyond the default distance threshold.
For 3) Make sure you have neighbor constraints enabled between the sections - you only want to disable those when you want to create your own constraints, i.e for a door where you want to position the hinges precisely, or the hood, or the boot, etc...

If it's none of those, it'd be really helpful to see a file. If you can't share it publicly, file a bug and upload it there so I can take a look.