Question about Bissell SpotClean Professional

This is the fresh water tank that also moves, but it doesn't matter because nothing is leaking

No is not the case with me, it is held with the red handle

is the same for me....

No, turn the red carrying handle all the way forwards and then all the way back again to lock it in place

In my case, it sits firmly and stably. I place the transparent container on the appliance and move the red bracket as far as it will go, which fixes the container in place.