An "online" UPS is what you need. These have circuitry that converts the line voltage (which is probably bad in your case) to DC, and then recreates the AC at its output. Without this, your UPS will often switch to battery power, allowing its batteries to discharge during use. This switching of non-online UPS will also create blips in the power output that can damage the motors in the fridge.
You also need to make sure that the UPS creates a good-quality sine wave output. Cheaper UPS will create a square wave, or a very unsmooth AC waveform. Not having a smooth sine wave output will cause damage to the motors in the fridge.
The amount of power you need is a minimum of the volts multiplied by the current of your fridge, 230 times the current that it draws. Your UPS is rated in Volt-Amps (VA), which is a slightly different quantity. It has to do with the apparent power used by your load. Modern devices will have an apparent power very close to their real power, though older devices (especially motors) will require much more apparent power than their "real power", so I'd suggest over-sizing your UPS by 20-30% for this.
In addition, motors often will have a large "in-rush" current when they first start up. This can easily be double the power required once the motor is up and running. Perhaps the 1 A already factors in this inrush current, since 90 W is less than 0.5 A at 220V.
With your UPS providing 600 VA, and your fridge needing (1.0*220)=220 W, your UPS can likely supply sufficient power. The concern are if it will damage your fridge's motors, and if the battery has enough capacity to last out the voltage swings.
You can measure voltage and frequency with either a good-quality multimeter (e.g. a second-hand Fluke 77 on eBay
or a plug-in "Kill-a-Watt" type of meter.
Cheap $5-$50 new no-name Chinese-made multimeters are usually not really safe for use on 230V
Personally, I doubt a 10% difference in voltage will be critical for any of those devices apart from the Japanese 100V items, that could overheat. n.b. EU supply = 230V+/-10% US supply=120V+/-5% so running a nominal 100V device at 126V might be cause for concern.
Japan has a mix of 50HZ and 60Hz supplies so I'd expect Japanese made 100V appliances to be happy with either.
Best Answer
It should work fine ( 60Hz running on 50 sometimes doesn't work) but if the motors are synchronous to the power grid it will run fast. Wether playback at 1.2x normal speed is a problem or not is up to you. If you are recording and playing from the same machine then it won't matter.
Grid-synchronous timing was very common decades ago (analog tv for example) - the AC frequency was stable and reliable. When devices moved to DC motors and digital control they stopped caring about the mains frequency and just generated their own timing signals.