for short run times you would probably get away without adding an extra fan, but for peace of mind id just stick a fan on it running all the time.
older motors that aren't made for inverter use do tend to run a little hotter on an inverter then if on mains, so a bit of extra cooling wont do any harm, plus will help spread the heat around the workshop keeping you warm in the winter

if you've got access to the equipment you might as well check the speeds and see which one is telling the truth. Have to remember that without feed back the inverter doesn't really know what speed the motor is doing, so its worth knowing how accurate its guess is.
from my experience very few setups will be 100% accurate on speed so iv never paid all that much attention to the speed the inverter 'thinks' its doing. a few RPM's here or there doesn't really matter to me, I'm more interested in what the machine on the end of the motor is doing. iv seen more then a few blocked pumps sit there humming away stalled , whilst the inverter thinks they are doing anything from 10-250 RPM.
braking shouldn't be that difficult to set up, just need the appropriate resistor and to make sure you have a reasonable time set for the stop.