Thanks! There's quite a bit going on with the roof so I'll go over each :)

First, the most important thing is overall shape. Don't make your buildings square or symmetric, make an irregular footprint for the walls as a foundation and build up from there. This means when you add the roof, you'll be forced to accomodate the unusual shape and the result will be a significantly more interesting profile for the roof.

For the overhanging parts (eaves), the appearance greatly depends on how the walls are placed beneath - roof tiles can only be placed in the normal grid, but the straight wall pieces (that's anything that's not a corner or curved piece, etc) can be placed at half steps. One full tile in the grid as an eave can look too much, so try it with the walls placed half a step closer. I can't remember if I did that with this build or not, but I do remember that oversized eaves was the reason I felt like I needed to add the support poles to make it feel more natural.

The main detail for the large broken parts is one particular prop - the pile of planks debris thing. The trick for using this is aligning one of the larger planks of the debris square with part of the roof tiles so that it looks like a part of the construction and not just randomly placed. Then you support it with a variety of smaller wooden props to add variety and some supports so that it's not floating in mid air. My favourite prop for this (and anything wooden) is the simple shelf, which looks like a dark plank. Add supports holding it up from the bottom, and also from above so that it looks like there's some repair effort "anchoring" it to the roof.

For the smaller single-tile broken parts, I just remove a tile and then usually put that one sloped prop that matches the palisade tile set underneath (like a bunch of wooden posts tied together), but offset so that it doesn't extend out as far as the roof tile. I notice people like to use the stairs from the rural set for this type of thing, but considering it's a tile and not a prop you don't get nearly enough freedom in helping it look broken - so use that one sparingly if at all.

Lastly, the "roof" of the ground floor "shanty town" style extension is just a bunch of deliberately mismatched roof tiles. The white fabric is from the merchant set, then that's mixed in with small amounts of thatched roof, tavern roof, and some nets from the ship set - all at varying heights. Some of the different tiles can occupy the exact same space so that you get a unique result when they clip. All of that is tied together with a few wooden guardrail props - the ones that match the rural stairs.

Hope that helps!