A focal length of 100-105 mm is probably better for 6x7, but an 80 can work, as ic-racer said.
Often the hole in the enlarger's lensboard is threaded and the lens simply screws on. In other cases, it's a smooth hole and you need a retaining ring of some sort that threads onto the lens and essentially clamps the lensboard between the lens body and the retaining ring. In some other cases the ring has screw holes like the one you have and can either be fastened to the lensboard with screws in those holes or just used as you would a retaining ring.
The 135 would work for your 6x7 negs but the magnification will be a little low, it's more commonly used for 4x5.
The common mounting diameter is 39 mm but lots of lenses are different, for example, the 135 El Nikkor's body is 50mm and (when new) Nikon supplied an adaptor that is 39mm. The lens can be used either way, but I like using it with the adaptor better on my enlarger.
Yes, generally you use the format's "normal" focal length but there are a lot of reasons to vary from that, for example, if you like small prints, a longer than normal lens will work better. On the other hand, if you are trying to print large you may get to the limit of the enlarger's column and find you need need more magnification (which you get with a shorter focal length).