The fungus is just because the post are getting wet frequently. Don’t know how closely it is related to mushrooms but it is a plant.Just google “wood destroying fungus” and you can get a degrees worth of information if you want.
The cost of fumigation may or may not have much to do with the extent of the termite activity…probably not. It’s more related to the size of the house. If the seller isn’t paying for it , you can often get it cheaper than the first bid if only one termite co. bid the job.

On that house,you probably don’t have a huge problem with the attic but should question the inspector thoroughly for clues as to what the colonies look like and if they are active, where and what have they done,still active or not. On very old houses I have seen rafters,the part that holds the roof sheathing up, that were hollowed out from the fascia to the peak. The wood pieces were like a paper box with nails stuck in it. I have seen walls in kitchens and bathroom where subterranean termites had ventured up to eat several of the studs too.

Rot from serious water damage from leaks in roofs and exterior walls, pipes, shower stalls and the like is much more prevalent than serious damage from termites. It’s in poorly cared for buildings…usually rentals. Serious structural damage from termites is more rare but they do often make trim, wood items from porches and decks and such look like crap and sometimes open up houses so water drains in, causing more damage.