Solost yes I do think that the phone calls to the DCs are all about his needs, not theirs. I also think you should intervene on their behalf and stop an activity that they don't want to do. As you say, most DCs of any age don't like the phone and I expect they have come to dread these calls. I think if he had to call them on their mobiles only, his calls would drop off.
WRT him seeing them in your house, I don't think this is about the DCs, because I heartily agree that in actuality, this situation is potentially more damaging and confusing for them, with their Dad popping in and out whenever it suits him. They will have friends who have more boundaried relationships with the non-resident parent and I think this is making it worse and giving them false hope.
I think in his small way, heartbreaking though it is, your DS thought he was being helpful (and hopeful) by summoning his Dad around to fix the television. He might even have been a bit cross that you went out, although obviously that was entirely the right thing to do.
From the DCs' point of view, I think they need to accept that he's not coming back and therefore a new regime must be put in place. I don't agree that him seeing them in the house is helping them at all.
I suspect you think it might be helping you Solost because you still want to see him and because it puts off the risk of him introducing them to the OW. But now that the DCs know about her, all you can do is ask that he doesn't do that, for a time.
If you really do want to detach from him and mean it, I think it might help if you examined your true motives for letting him come and go like this. I would absolutely understand it if you still wanted to see him, but let's acknowledge it and deal with it and then we can all tell you that this won't help you in the long run.
Whereas I feel we would be doing you a disservice if we continue to collude with you, that this is about the DCs' welfare.