Will 1K inverter work microwave?

Probably not, get 1500 watts sine wave.

The short answer is. NO

A "700w " Danby wants 1050w input on pure sine wave, less on MSW.

My "1000w" PSW inverter will run the 700w Danby but is maxed right out.

Most MW do not use less power at lower settings. They run full but for less time. Ie longer time off between times on. some Panasonic inverter types will though.

Use the divide by 10 rule for amps drawn. 1000w draw is 10amps DC from battery for however long it takes. A six minute microwave job at 100a would be 10AH from the battery bank.

Next issue is how low the battery voltage gets with a 100a draw. It has to stay over 11v or the inverter will shut down. As soon as the 100a starts voltage will drop to say 11.4 then slowly go down from there. Will the potato get done before it hits 11v?

The bigger the bank in AH the more you can draw without it dropping to 11v. with smaller bank you can still do some before it hits 11v but you have to start with the bank more full than if it were a big bank.

It would be close if you drop the power down. Look on the back, the 900 watts might be cooking power and not all the power it draws. Give it a try.