Doc the block heater should be a pretty "dumb" part that should just work unless 1) the power cord is shot or 2) the heater element has burned out. Seems to me simple continuity checks on the cord and the element should suffice to locate any problem. The cord is just like any normal 110v electric cord and I strongly suspect the heater element is functionally identical to a hot water heater element. If the latter is true in the past I was easily able to id bad hot water heater elements but checking for continuity.
As to your PNs your best bet is to check with a local dealer as the online parts manuals are not very helpful. As best I can tell:
4557686AB 1 ED0 - cannot find that # in the 06 KJ parts manual copy I have but the ED0 engine code does not match the ENR engine code that's supposed to be for the 2.8L CRD
55037539AA is not the block heater it's the viscous heater
56041304AB is a block heater for a gas engine. I do not know if it will fit the CRD
Check down where the cord attaches to the heater, see 1st pic at
viewtopic.php?f=98&t=74594 . It's been several years since my son and I replaced his block heater cord so I don't really recall how it attached down there (plug vs regular screw fittings) but it may be that a regular hardware store 3 wire cord can be used. In any case the local dealer had it in stock, don't have PN, for like $25. It's a flat 3 wire with insulated wires contained in an external rubber like sheath and that sheath is prone to cracking if it's left wadded up attached to the dip stick as it came from the factory. If the sheath is not cracking and the wire has appropriate continuity replacement is not truly needed.
Strap - I have no clue what this is. The only strap my son and I saw was a simple reusable zip tie holding the bundle heater cord to the dip stick. I do vaguely recall some sort of metal clip, possibly a wire stand off clip, down near where the wire hooks in that gave me a bit of a fit but it was not anything that should need replacing.