The vehicle is an x230 model, and the engine is generally referred to as a 2.8idTD (injection direct Turbo Diesel).
Windscreen wiper arms are usually mounted on a taper. Wiper arm puller kits are available on Ebay, and probably from local accessory shop. I think that the motor has tapered splines. With taper fittings. a light tap on the outside once tension has been applied via the puller sometimes helps, if attempting this support opposite side with second hammer, or similar heavy object.
I am afraid that I looked at the wiring with horror. but then I have been described as fastidious. Is there really a battery hiding in there? If as you suggest the red wire connects to battery positive, I cannot see a fuse. A fuse should be fitted as close as practicable to battery positive.
@bugsymike any thoughts from your wealth of experience?
Do my best.

You should be able to remove the wiper motor and linkage as one unit if lucky.
The large nuts at the wiper spindle ends need removing , keeping the order of bushes and spacers correct for the return , there will also be some mountings bolting the motor via rubber insulating bushes to the vehicle, then of course the wiring plug, you then push the linkages back through their mounting and hopefully wriggle the whole thing clear to work on.
If you can get the whole unit out, I would then disconnect the motor at the end of it's crank if possible.
Note the reason for that rather than at the motor spindle is when reassembling you may find the wiper arms are cleaning the bonnet etc. as out of sync.

Once motor is disconnected you will be able to see if it is the linkage at the spindles that is seizing or the motor it's self, of course it may be both.

However with care and lubrication you should be able to free it all off.
Generally speaking I have not found many motors worn out as they are never running long enough at any one time.
However if motor has been left on and spindles seized then it can burn the electrical windings out.
Once all sorted and assembled , check the wiper when turned off at the switch that it correctly moves to it's park position and note where that is.
I see the wiper arms are already off, but when you reassemble do not fit arms until you know for sure where the "park position" is to avoid going off the windscreen area and causing damage.
Also make sure the arms are correctly fitted on to the tapered splines and nut tightened correctly.
A "windscreen Specialist" didn't on one of my daughters cars a VW Golf and on turning the wipers on, the arm promptly broke, luckily I was watching him so he couldn't blame a faulty part, so it cost him around £80!