Should I build a deck over my existing concrete patio or other?
It's quite a drop off there on the manhole side. If it were me, the priority would be to build steps of some kind there--or a railing.

Anything that is well-drained will not rot. Rot only occurs when something sits in water.

You could certainly deck the porch over if you wanted. My pet peeve is people who just stick wood in the ground. The main thing to consider is how you are going to support the deck. The porch is so tall, that you could just anchor it to the sides, so it just hangs down. Then maybe just have two footings for the steps. Or you could put a skirt of steps all around and have footings every 3 feet or so.