You still need gas exchange yes.. the only time you don't is with artificially supplied CO2.
circuation fans are still useful as always.
if the tent exhausts to the room, you need to control the entire room's climate anyway.. so outside will save space inside the tent. In an extreme context where you cannot control the temps in the tent, inside might help a few degrees. there will be an offset of temp inside the tent vs outside related to how much air is flowing out/in and how much heat the light is producing... more airflow = smaller offset. 25-30C is your goal inside the tent with a corresponding RH% that results in a good VPD (vapor pressure deficit).
in a tent where plants take up all the space, i prefer my equipment outside. so as not to take up space. i work in a 10x10 and use hafl the tent.. the equipment is on the open half of tent. There are some advantage to having the dehum inside... it's more efficient at higher RH so if it does spike, it'll work faster inside the tent rather than outside where it'll be 5-7% lower in my context.
so.. start with whatever, then see how it plays out.. adjust how it is setup if necessary.. may be som trial and error when you start using it, but you'll get it evened out.
the ac unit definitely needs to exhaust outside.. usually they come with a window adapter or something. it generates more heat than cool air..ACs are not efficient and physically impossible to be 100% efficient (which would be heat produced = to cool air produced). Same reasons a perpetual engine is not possible.