I've become fascinated with ponds lately, and have been researching how to keep a well maintained pond w/out filters, aerators, or water pumps, because all the plants work together, using mother nature to keep the water clear and beautiful.
Yestarday I set my mind into creating a water garden...
I would just compost that as it is. Just spray it with water every couple days and turn with a fork several times a month. It would take a long time to for worms to break that down. You'll have to put small prtions of it into your bin at a time.
I'm sure its ok. On a thread I read that snipping off the tips of the vines keeps the fruit sweeter. Don't let your melons take over. Snip some vines if it's necessary.
We got lots of figs here too. I love them! The only think I dislike is that if your lips touch the skin of the fig, you'll have little spikes stuck on to you.