There are discreet graphic cards with passive cooling available. The power-hungry models fitted with dual 120mm fans and a large heatsink are not too noisy either.
Some GPUs have fans that spin down entirely under light load (Asus calls it 0db mode), and only spin up the fans when under moderate to heavy loads.
Yes. Also, at least With NVDIA cards, you can specify a temperature target to the driver. I think the defaults usually run the chips at ~70C.
I guess the fans are actually mostly 100mm in 2x fan configurations, manufacturers seem to have many custom solutions for blade configuration etc.