A lot of misinformation here...
If there was clouds of smoke coming from the exhaust under 3K, then there was a problem with the engine or carburetor somewhere. A worn engine generally will smoke at high RPMs but be fine at low. If a rotary is smoking at low RPM, it is
really worn. An engine that worn would be unbearable at high RPM as the massive white/blue clouds of oil smoke would blind anyone behind. More then likely it was a carburetor problem. The old Nikki carb had a tendency to stick the secondaries a little open, dousing fuel into the engine at low RPM. This not only makes it drink fuel like no tomorrow, but also washes the lubrication film off the chambers and allows oil to bypass the oil control rings. Thus high oil consumption and smoke.
The lack of torque under 3K is relative as well. While the rotary is a high RPM engine, comparing the dyno charts of a modern engine (but NOT the Renesis) shows a very linear torque curve. The older carbureted engines had a seeming lack of torque, until you consider that they are in fact 1.1 or 1.3 litre engines. The simple fact is that if you expect to be able to floor it at low RPMs and get moving it ain't going to happen. Go down a gear like you should.
Mazda's rotary engines use a metering oil pump to supply a small amount of oil to the apex seals for lubrication. This oil is burned as part of the combustion cycle. From the factory, these pumps are adjusted to supply the minimum amount of oil necessary and therefore should not smoke. Sometimes people crank them up, or start premixing 2 stroke oil into their fuel. If the pump is cranked too far or there is too much premix (especially combined with a rich mixture) then there will be smoke.
There
certainly is a redline. It's clearly defined on the tach. And there's a loud joybuzzer to let you know you're there.

Over revving can and does completely trash engines. Without balancing, clearancing, windowed bearings and oil mods then 8K (9K on later engines, 10K on the Renesis if I remember correctly) is the redline. If you want to go higher, then the engine should be built for it. Otherwise at high RPMs you will start to get eccentric shaft flex which can cause the tips of the rotors to come into contact with the housing, or the rotors can lean over and contact the irons. Both being very bad things.
Does the rotary run hotter then an equivalent sized piston engine? That's a good question and in my opinion the answer is no. The factory thermostat is 84 degrees. Do they produce more heat? Absolutely. It's a high revving engine that fires 3 times per rotor revolution and does not have the benefit of the incoming fuel charge cooling the exhaust area like a piston engine does. Also keep in mind that the only way to cool the rotors is with a set of oil jets that spray the insides of the rotors from the eccentric shaft. Thus the need for an oil cooler which accounts for about 30% of engine cooling. For some idiotic reason Mazda tried a oil to water cooler in the early '80s on the RX-7 which was a disaster. Soon after Mazda went back to a proper oil to air unit. Overheating
can be instant death, but unless it is severe, the engine will survive. If the overheating is bad enough then you can warp rotor
housings or irons. The result can be coolant leaking into the engine and the need to rebuild (and it's rare to get usable parts from a water pumper if they are left to sit any length of time...).
As for pollution, Mazda was able to pass emissions in the '70s with out cats due to the low NOX emissions of the rotary. They used a bizarre thermal reactor system to deal with the hydrocarbons. Later on they went to cats, and fuel injection cleaned things up a lot. But still, it's a high overlap engine and it does pollute more then it's piston counterpart. The Renesis made major improvements in pollution by virtually eliminating port overlap through moving the exhaust ports to the irons. The Renesis is much cleaner but unfortunately the side ports really limit the amount of power available from the engine.
Yes, gas mileage is terrible.
