Likely a bird is building its nest in your chimney, and the sound you hear is dislodged mortar from its nest-based activities. I had this in my previous house, for a few weeks every year, normally between 7am and 9am.
Lucky it didn't rain before he got the tiles on. When mine was done a few months back we got 36mm of rain in 5 hours with 40mph winds - there wasn't a tile on the roof, just membrane.
I'm just getting a fan installed in the gable end with a 150mm hole and a vent on the outside. Controlled by a Wifi adapter so I don't need to go up there to change the settings.
Except I didn't. I commented one hour after the previous post, which appeared earlier today and was deleted after I commented on it. I edited mine to reflect that, as you can see.
It depends on the temperature difference. If it's small, air will flow upwards for a time and the house will cool. If it's large, air will flow both ways and the house will heat up. I intend to fit an extractor fan in the loft to dispel the nuclear reactor levels of heat we get on hot days.
Mine was certainly improved by removing the chimney and all those other horrible protrusions surrounded by manky leadwork and plastic. But I imagine if you have a more rustic house a chimney is more of a feature.
I can't see any cracks, just a few places where the pointing has crumbled away. That said, chimneys can be a pain - not from falling down, there's no possibility of it doing that short of a tornado strike - but from leaks and damp and the general maintenance they require. I had mine taken off...
You post like we can't see what you wrote.
"never paint masonry - & never paint plastic."
So don't pretend you were talking about difficulties or exceptions. There is no issue whatsoever painting properly prepared masonry or plastic with the correct materials.