what is the RPM (revolutions per minute) of an aircraft engine ?

Comparing piston engines to turbine engines won't get you very far. Turbines spin at very high RPMs, don't know the specifics, but IIRC, it's in the 10's of thousands, a turbine engine is simply spinning around, while your reciprocating piston enigine found in cars and motorcycles has parts moving back and forth trying to tear each other apart.

Typical aircraft piston engines redline between 2000 and 2700 RPM. That's about as fast as you can turn a prop before tip speeds become transonic and lots of thrust is lost.
The speed at which the rotating components of a turbine engine spin is not a function of its power, it is a function of the diameter of the rotating assembly.

The larger the diameter, the lower the RPM. The smaller the diameter, the higher the RPM.
For instance, the JT8D turbofan engine has twin rotors, N1 and N2.
The N1, which includes the fan, low pressure compressor, and the low pressure turbine has a maximum RPM of about 8,000. The N2, which includes the high pressure compressor and the high pressure turbine has a maximum RPM of about 12,000.
The RB211-22B's fan rotates at about 3800 RPM. I've forgotten what the max RPM's are for the intermediate and high pressure rotors.
The Allison 501D/T-56 series engines operate at 13,821 RPM. These are single spool engines.
The reason for the speed being tied to the diameter of the rotor is that you don't want your blade tips going faster than around Mach 1; so the bigger diameter rotors spin at lower speeds. Above M=1 and the blades lose efficiency. The same goes for propellers, larger props turn slower.

how many times per minute does the spinner rotate

Max NP=1200 rpm (for a Dash 8 100)

And for the PW120/121 spinning this propeller;

NH= 33,300 rpm@ 100%
NL= 27,700 rpm@ 100%
Power turbine- 20,000 rpm@ 100% NH

At 100% RPM the RB211 produces the following RPM.

N1 4500 RPM

N2 7000 RPM

N3 10,611 RPM


RPM of typical airline's turbofan engines are around 8,000 to 10,000 rpm...
The CJ-610 (Lear 24-25) is a 16,700 rpm engine - military designation J-85...
Centrifugal compressor engines, have generally high rpm, some at 20,000+
Examples would be a J-33, J-69, or RR Nene...
Propellers on turboprop engines would turn too fast for typical turbine rpm, therefore such engines have gears reducing shaft rpm to acceptable limits for the propellers...
xxx
Note also that "100%" is not necessarily "maximum" rpm...
Some manufacturers designate 100% of N1 (or N2) as being xxx rpm...
Maximum (red line) could be i.e. 108.5% on some given types...

Courtesy of -wikipedia.org,google images