in s.a. generally motors up to about 4 kw are designed to run in star
and above 4 kw in delta.
but as mentioned the rating plate must be checked.if it says 380 volt star and 230 volt delta then it is must be connected star in s.a. and delta in a country with 230 volt 3 phase . these windings are designed to handle 230 volt maximum.these are normally american motors.
regarding the single phase vfd,s i have only come across the models that supply 230 volt 3 phase output. its probably easier to manufacture. the motors should be connected in delta. in star there would only be about 130 volts across each coil.

regarding the 3 phases and neutral connection to a motor,i have never seen it. what application would it be used for?
with 3 phase heating elements in star connection you could run it without a neutral ,but if 1 element blows the other 2 would only have 190 volts across each one. with the neutral connected to the star point it would stay 230 volts even if 2 elements are faulty.