Electrical – can we use UPS as stabilizer for 1.5 ton AC

No.

You definitely want to put the humidifier on its own circuit, or a circuit that is not shared with two powder/bath rooms. You could look for a convenience receptacle in the basement and determine if it's on the same circuit. If not, you can probably come out of that for the humidifier. If the humidifier pulls it's full 7A rating when it starts, you probably want to avoid having it share a lighting circuit, as the lights could dim when it turns on. That can cause premature wear on ballasts and greatly reduce the life of any incandescent lamps you might have in use. Take care to know exactly what else is on any circuit you find in the neighborhood.

NEC requires wiring devices, such as the relays you're talking about to be listed and approved. Assembling something to cut the power to the UPS when the humidifier kicks in using all listed and approved parts does not constitute a listed and approved device. Your approach, while very creative gets a little too far into the "Rube Goldberg" brand of tinkering.

My advice is, have an electrician install a single use receptacle for the humidifier on its own 15A circuit, even if that's slightly overkill. If your panel will not accommodate this, and tandem breakers aren't a possibility, then consider increasing the size of your panel and / or service.

Two bathrooms on a single 15A circuit is problematic enough, it sounds like you need to bite the bullet and get a few additional circuits where they're needed.

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.