the fan is installed and I have a few follow-ups:

From the crawlspace, I can see some daylight between the opening in the drywall ceiling and the fan housing. What is the preferred type of caulk to fill this gap? Is spray foam appropriate for this?

Also, I reinstalled the aluminum ductwork but I'll be back in the attic when I figure out what the permanent solution is to the duct. The existing duct is full of dirt and dust. I'll probably swap it for a pvc duct. Is there anything special that I need to do when I connect the aluminum duct/exhaust from the fan to the pvc?

thanks.

A fan duct should be rigid steel, NO flex, NO plastic with as few corners as possible, and where they are, as gentle a corner as you can manage - think two 45 degree bends vs. a single sharp 90 degree corner.

Venting hot humid air into your attic seems like a nice recipe for mold and for ice dams in the winters.

A bathroom fan vent should vent all the way to the outside of the house - through a wall or the roof.

The vent in your roof is designed to keep the air in the attic cold in the winter and from accumulating too much moisture - circulation. Hot humid air from your bathroom fan is contrary to both of those objectives.

The fan body forms part of the vapor barrier system - it needs to be tied into the vapor barrier that I presume exists between your drywall and the attic with tuck tape etc. again, to keep the warm air from your bathroom from escaping into your attic.