Ridgid is really the only way to go especially over long runs. We usually spec 4" sched. 20 PVC pipe as it comes in longer lengths than 4" metal does around here , though elbows can be tough to source sometimes. Unfortunately most contractors / HVAC guys will use flexible corrugated hose because it's cheap and fast. If it's a luxury project they'll splurge for the flex aluminum instead of the plastic kind. This type of pipe can cut a fan' effectiveness in half over long runs. Little thought is really given to these fans in most homes today. They are often undersized for a given bathroom and poorly located too. The crappy pipe detailing makes a bad situation worse. Panasonic's website has (or used to) a pretty good tutorial on how to properly size a fan, where to locate it and how to properly pipe it to the outside. I think much of the problem is cost and ignorance. Most people know you get a fan in your bath , but when pressed they won't really be able to tell you its there to expel warm moist air from your home, not smells. They assume that the $34.95 version will be fine for them and a quick & dirty install will get ya out the door for a hundred bucks. The reality is, many master baths, and some hard working kids baths need a much larger fan than 35 bucks can buy. We are often talking $100-$200 for an adequate model, more if you want features or quietness. Add the increased piping cost and labor for the proper venting needed on higher capacity fans and this can quickly become a $500 line item - which starts to look crazy for something as pedestrian looking as a bath fan. Timer switches are also a very good idea as most fans even properly sized ones need to run a while after you've left the bath to completely exhaust the moist air.

Ignoring the relative deficiencies of down-draft hoods, control compatibility is a "maybe." If Broan used a triac type control and the Fantech uses a straight-forward induction motor, and the Fantech is approximately the same power draw as the Broan fan, then they should be compatible. Other types of controls might also be compatible. You may not want to experiment without first contacting Fantech to determine the FG8's compatibility with different control devices, and technical support at Broan to find out what type and rating of control is used with their hood. kas

there are two separate issues that need to each be addressed entirely on their own. in all of this, remember that your fan duct is a chimney and reacts accordingly. you usually have warm air flow and waste even when not "using" it. if you have condensation and it's all in cold weather, insulate the thing. Not with that trendy gimmicky thin plastic junk but with a whole lot of plain old fiberglass. a lot of it. reseal any seams first, perhaps with brush on goop and fiberglass mesh. the water damage is a separate deal and I would not be any way qualified to suggest anything concrete without eyes-on. both issues do seem to be from poor installs. the s-trap is funny, though.

If it is "just" a joist it can be boxed or perhaps a sister joist depending on whether the exhaust just kisses the joist or requires it to be cut out. Make sure you are advised by a very knowledgeable contractor. A roofing contractor may have the most experience. "Plan B"n is a nice idea except that it may require major foot-print revisions.