The window area is the area of the section where the wires' cross-sectional areas sit.
Should it be both added together.
There are no multiple window areas. There's only one window area and it's generally given in the core (and accessories) datasheet as AN or AW. The following is from TDK's ETD39 datasheet:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/917qE.png)
The image you nicked from the linked question doesn't correctly show the window area (I had edited @Transistor's answer there, BTW). The area marked with red diagonal lines is the maximum you can get, theoretically. But practically it's going to be less because there's a bobbin. That's why you should always check the datasheets.
I found one of the transformers in the 1000kW inverter. Where the bobbin size almost made the window area negligible. But still the transformer successfully worked at its full power. How is it doing that. Shouldn't it's power capacity decrease as window area gets small?
1000 kW means, if we assume the output voltage is 250 Vrms and the load is pure resistive or power-factor-corrected, 4 kArms. This current level is so high that there's no way you can carry it with those thin wires (Even if we assume you meant 1 kW and made a typo, still the above comment holds). Despite the fact that the transformer may belong to an HF inverter, the skin effect wouldn't allow the designer to use those thin wires to carry 4 kArms.
Before everything else you need to understand the magnetisation (flux swing, energy transfer, etc) and the relation with frequency at first. I admit, winding your own transformer and taking measurements on it is a very good way. The area-product formula which is available in different forms everywhere is based on some assumptions which may or may not apply (fully or partially) to your needs. Yes, it gives a good starting point but there are many other things to consider.