A C182 pilot reported engine failure in flight and diversion to the nearest airport.

Narrative

We were cruising on a flight from ZZZ1 to ZZZ2; as a fuel stop along our route. What I am about to describe happened 20 minutes prior to the adverse event I am going to describe following this; while cruising we felt a slight 'thud' and smelt a faint chemical smell for approximately 2 minutes; everything seemed normal and no abnormalities were present; we chalked this up to turbulence or the two large dogs in the back possibly jumping or moving. (This will become important later)However; at 10;500ft MSL about 20 miles southwest of ZZZ I noticed the oil pressure gauge shift to near the bottom of the green arc. And about 20 seconds later it dropped below the green arc and we felt an engine roughness; not so much a decrease in power yet. We looked at our ForeFlight advisory glide rings and realized we were not within gliding distance of ZZZ (the nearest airport) so I suggested we climb the airplane as high as possible at Vy speed (we got up to 12;300ft MSL). As ZZZ slowly became within gliding distance; the oil pressure gauge continued to fall closer to 0. I suggested we [request priority handling] and worry about the paperwork later; but this didn't seem to convince him as we still had our engine and it was producing power. We got over the airport at 12;300ft MSL and that's when I stated our intentions on the CTAF that we were steep spiraling down to land on the runway. Around 11;000ft the engine started running very rough and I suggested we turn off the engine before it got too dangerous or violent and caused damage; as I knew we could easily spiral down with no engine and glide it to the runway; a commercial maneuver we have both practiced numerous times. However; the pilot I was flying with was not convinced to turn off the engine until it got very rough and smoke began coming inside the cockpit. (Later on he would state that we should have turned off the engine earlier; I believe he learned a lot from this experience).We were now around 9;500ft MSL when I pointed the smoke out to him and declared on CTAF that we had an engine fire and announced for everyone to clear the runway. We then pushed open our windows while simultaneously pushing the nose forward in an attempt to put out the fire; the other pilot had controls at this time and I was shutting off fuel to the engine. The fuel tank selector valve would not move from 'RIGHT' to 'OFF'; we swapped roles and I continued to fly the airplane down in an attempt to put out the smoke even punching through a cloud to get it cooler. He wasn't able to shut off the fuel tank selector so we swapped roles again; as we had decided this was going to be his landing as he had over 100 hours in this aircraft specifically; where this was only my second flight in it. I then was able to get the selector to budge to the 'OFF' position. I then squawked XXXX and [advised ATC] on frequency.Once we reached approximately 4;000ft MSL the smoke coming inside the cockpit had calmed down and our engine stopped windmilling. The other pilot continued the approach to land and did another two spirals and slipped the aircraft on final to get us low enough to land. He came in fast with no flaps and we used up a lot of the available runway length; at least half. We pulled off on whatever taxiway shut off everything and hopped out of the airplane; we also instantly pulled the dogs from the baggage compartment. We were then met by two gentlemen from the FBO with a fire extinguisher and they put out the remaining smoke coming from the engine. On the ground; we noticed the spinner was missing and we believe that was the 'thud' we heard 20 minutes prior to this event. We are not sure if it punctured something as it flew off and caused a gradual oil leak; but this is the only guess we have about the two events being related. After removing the cowling; near the rear two cylinders of the engine it had thrown a cylinder rod right through the top of the engine; leaving oil everywhere and a massive hole on top of the engine block. We also noticed we must have popped the nose gear tire during landing via intense braking efforts. After being met by authorities; firefighters; and ambulance crew. The aircraft was then tugged to the FBO.