Owning your own home

That's taking the piss.

This is me doing near exactly the same thing.

I don't really know what they are doing, but that gives me the eebiejeebies

That looks like he's been holding the SDS 90° to the wall? What did the plaster look like when it was off? Any big continuous chunks?

I doubt that your house will fall down - mainly because at the very least there will be a soldier course of bricks above he window.

questions I'd want answered in your situation:

1. what happened to the large chunk of wall that appears to be missing (Bottom right hand corner)? How is this going to be made good?
   
2. Is that cementicious render behind the top coat of plaster (grey stuff)? It doesn't look like normal bonding plaster (It could be - depending on the age of house) could someone have tried to "fix" a damp problem previously? if so how is he going to make sure that the same issue does not re-occur?
   
3. Is the air brick that is visible on the outside of the wall going to be left clear and unobstructed?
   
   

Also if the wooden floor has been left in situ check it for damage before releasing the balance of payent as IMO a sheet of Tyvek is not sufficient protection. In that situation I would have a sheet of (clean) corex with 12mm ply on top with a dustsheet on that as well