High eurorack,
I would use 2 large cable ties to hang the filter.
And yes the fiter can be placed outside the tent aswell and let the fan blow the air into the filter. But these kind of fans are better for sucking the air then pushing it through the filter. So both options are possible but for the lifespan of the exhaust fan you can better let it suck the air through the filter so keep the filter inside.
Happy Growing! 😋