best place to mount in-line fan ?

[Rusty Trichome]

- where in the hood duct is best place to put fan- pulling or pushing-

Pulling. When pushing, the fresh air can easily escape through vent gaps and such. The fan would 'push' the heated air out of the vent system and right back into your growroom. In other words...it lowers the effeciency of your exhaust.

also will have a carbon filter for exhaust- could I have a 2 way connector to for hood and room exhaust or do I need to have 2 different exhaust ports- a 2 into one would be nice-that way I could use one carbon filter-

Air and water usually take the path of least resistance. (one side of your equation will restrict flow a little more than the other) If you have a strong enough exhaust fan, no big deal.

Heating it during the day is done via the lights. At night though...you'll need that heater.