As I understand it:

Catacombs are underground cemeteries - they can be anywhere. If dead are being buried, then there can be catacombs. As far as transitioning between the two, I don't feel the need to suspend disbelief in that there are entrances from the catacombs to different areas in the world. It works at a base level. Could it be better? Sure, but it doesn't make me think that it couldn't work. We also have the idea that kingdoms were built upon kingdoms from the second game coming into play.

Irithyll is the current name of the unexplored lower Anor Londo from the previous game. It was always there - we just never went there. There are clear and consistent links between the two area as you progress upwards.

The lore behind the profaned capital is that it was discovered by Sulyvahn in his younger years. It seems to be the establishment of another kingdom in the ages that have come and gone. The profaned flame is not the chaos flame as people are hypothesizing because the demon king soul has said that the chaos flame has not survived. Presumably someone has succeeded in imitating the first flame in the profaned flame. It's was discovered - and for it to be discovered, Sulyvahn had to brave the frigid Tundras of Irithyll (more or less written in item descriptions).

The Darkwraiths seem to be attempting to find and kill the watchers and everything to do with them. They guard the coal that is effective against creatures of the abyss so that it can not be taken - and attempt to fight their way through to the legion - notorious fighters of the abyss.

The swamp is also the Abyss Watchers base of operations, their headquarters. The wolf of farron is there to confirm this. They may go around crushing kingdoms where the abyss pops up, but that doesn't mean they live near the abyss at all times.