Your questions have raised more questions.
Are you sucking air from the room into the carbon filters, then thru duct to fan?
You could put the filter on the exhaust side of the fan.
Why don't you attach the T or the reducer, then the T directly to the fan?(eliminate 1 bend)you should be able to do 2 rooms w/1 fan as long as it is big enough.
Bends reduce air flow, so you will have more draw on the line with less bends.
Also heat rises, so you may want to suck air from higher in the room instead of down low.
Where are you getting your intake air from? With passive or active intake, that ail will be the same temp and humidity as the room it comes from.
Good luck