The output of your inverter has a square-wave. Many electronic products won't work because their power supply works from the higher peak voltage of a sine-wave.
The circuit is too simple to regulate its output voltage.
A cheap poor quality transformer has poor voltage regulation.
Maybe your transformer is designed for 60Hz so has a small core. Then it won't work well with 50Hz.
Today it just does not make sense to use a low frequency transformer. It makes much more sense to convert to high voltage at high frequency and then use a full or half bridge to obtain a "modified sine wave". That is what all commercial units do.