The metal with the holes in it between the framing and window appears to be old lead flashing. It is excellent flashing and the holes are irrelevant, however, the flashing should have been turned up, not over, the framing as shown in the last picture. Your window installer didn't include this detail change in his proposal; he should have. Have him reinstall the window with the proper flashing detail please. And no, caulk is not mechanical flashing.

Gotta see the outside but the H-Mullion on the casements is not a good sign to begin with for the longevity and approach of the window installation.

Making sure the sills are sloped to the exterior is always a good start. Reflashing may have been needed. You google why windows condensate and try to eliminate that problem. Flashing at the sill is not is not typically designed to catch water from the interior. This job may have problems on both sides as WOW has mentioned one concern there.

I would have your installer back, and have him do a total redo.

In the UK?

houzz.co.uk

Yes the UK