Good Luck with your search for a 260. Here is a pic of what a windlass looks like. The picture you show clearly does not have a windlass it only has the basic rode chute with tie off cleat. There is a lot of good info to read through on the 260 here...
We are most times Full water, plus gear and 1/2 tank plus of fuel. Generally when we go out its for days at a time on the hook. I do not have the Generator on mine and Ive seen other 260 pics that sit low like yours so i always assumed the genny made a big difference.
You need this one.
Water pump impeller
Part # 47-8M0104229
https://nuwavemarine.com/mercruiser-outdrives-parts/o-b-i-o-cooling-water-pumps/oem-quicksilver-mercury-sea-water-pump-impeller-kit-47-8m0104229/
No i don't think they should be Hot. I believe that is an indication that they are sticking when the ECM activates them and they are being worked too hard.
Definitely sounds like the IAC's. Changing the IAC mufflers may have highlighted that they were on the way out. Id try changing one IAC to start and see what happens. You will know for sure. If it does not fix it then carry on troubleshooting and you will still have a spare IAC for later on.