I know I can use the pose dots/library to copy and paste an entire pose quite easily.

But I want to copy only the pose of my figure's upper body to another frame, not the lower. How can I do this ?

Also, unrelated note. When I export to BVH, every frame in my anim seems to become a keyframe. Is this a bug? It's very annoying.

I don't know about copying a partial pose, but you can save a partial pose to your pose library and then add it to the figure in the next frame.

Just open the Pose library. Click on the + sign at the bottom. In the window that comes up  select the parts of the body you want to include for the pose. It will ask you if you want to save the morphs, say no because you only want the pose, not the character morphs saved.

For example if you want to save an arm pose, select the parts of the body  from the collar to the fingers of the desired arm or arms. If it's only hand poses, save it with the hand and fingers selected.  Again, don't forget to cancel the "save morpns" portion when asked :)

Just to add to what Acadia said, when you click the "+" in the library pallet, the box that comes up will have a button "Selct Subset". That's where you can choose which parts of the pose to include. Un-checking "UNIVERSE" will clear all the checked body parts, which is sometimes handy if you only need to include a few parts.

If you want to use only part of a stock pose you have on disk, you can lock the actors that you don't want the pose to apply to, then after applying the pose unlock the actors (same trick works when applying a walk cycle). Having utility pose files to lock/unlock whole sections of the figure (eg legs+feet+toes, arms+hands+fingers, head+neck+eyes) can help when using this method.

Pose files saved as uncompressed pz2 files can be edited in a text editor to exclude various channels or actors. Once you get used to editing pz2 files you can even add various things like scale data, or data for the Body actor, which Poser does not include when saving pose files.