Electrical – connect a stabilizer to an inverter

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.

The key facts about your A/C are

Power Requirements  1/230V/50Hz
Cooling Operating Current   7 A

7 A x 230 V = 1610 Watts. UPS specs are in VA not W due to power-factor corrections which I'll ignore:

Your 800 VA UPS is probably not a good choice for a 1610 W load.