I toss crapped out pumpkins and squashes into my compost with no problem. Depending on how hot your compost gets or what your pile is like, you might get some volunteer pumpkin plants growing. I've had my pile totally kill the seed, and on the outside edges an occasional sprout.

Absolutely. For me, that would be the perfect excuse to get out my machete and hack away. :)

I usually avoid putting the squash and pumpkin seeds in my bin because of the volunteers, and likewise wouldn't bury them in my beds. But if you bury them deep enough so that you don't dig them to within a few inches of the surface, it shouldn't matter.

If you cook it, usually the seeds are sterile. Otherwise you will get many volunteers. It is otherwise fine.

Almost all once growing plant material can, and should, be put back into the soil if it is not used as a fuel by humans or animals. That pumpkin would be a good soil amendment, although the seeds, if viable, might not be.

Smash it with a hammer or something and bury it