Can I use a 220V 80W fan with an 220V to 110V 50W adaptor to make it work slower?
There are a few different types of voltage adapters, some of which are probably safe, and others will destroy the fan because the output contains a DC component. Check which type you are using.


Transformer: Transformers produce a pure sine-wave (other than esoteric Sola- type constant voltage transformers) AC output which is unlikely to damage the fan unless the fan stalls and overheats due to lack of air circulation. Since the rating of your adapter is 50 W, it is probably a transformer. Check also that the fan does not draw more than 2 A maximum, or it would exceed the capability of the transformer.
Diode: For resistive devices such as clothes irons, some adapters contain just a silicon diode. The output is pulsating DC, which is likely to destroy the fan or even cause a fire.
Thyristor: Triac and SCR devices do not really reduce voltage but slice the AC waveform into smaller pieces. Some are designed specifically for use with small shaded pole motors, as used in most ceiling fans. A danger with some controls not intended for use with motors is that the "chopped" waveform may not be equally balanced and have a DC component, with possibility of slow overheating, not immediately apparent, so perhaps a greater danger.
Series inductor: It is possible to use a simple inductor or "choke" to slow a fan, which should be safe, but the value of the inductor would depend on the current draw of the fan.