you can mate the fan to the filter if you have room, but there's really not a huge advantage to it, i have my fan sitting in a heavy cardboard box wrapped in old towels, with holes cut in the box for the hose. it cuts the noise considerably.
your room temps should drop anywhere from 5 to 10 degrees F.
the reason it will help with RH is that most of your RH in your grow tent is coming from plant transpiration. if you drop the temps, the plants won't transpire as much, so the rh goes down. it always drops when the lights are on and rises when they go off. if you can keep it under 50% lights on and 60 lights off, you should be good, 40 lights on and 50 lights off would be better, but with good ventilation you should be ok