How old is your child?
Get an old fashioned chip basket to fit a pan, that way you can put the basket into an empty pan, add veg and then water. You can lift the veg out with the basket and then a dc can empty the pan - if they are young let the pan go cold first.
Check out any help available - I'm in Wolverhampton and here you can order meals on wheels a any age, but it is delivered at lunch time so maybe not so good if the children are out.
You can cook pasta in any container, just put the pasta in a bowl or mug and then add boiling water. Leave for about 10mins.
Easy creamy pasta sauce, fry a sliced mushroom in lots of salt and pepper, add a dollop of cream cheese and a spoon full of the water you are using to cook the pasta, it will melt into a creamy sauce.
Is your microwave built in? If not get someone to move it into another room, or onto a kitchen work top.
Toast can be the basis of many meals, beans and cheese are obvious but also club sandwiches and to have with soup.
If you can get the microwave moved than you can cook beans, tinned food and fresh veg in a bit of water.
If you and the children can't wash up then buy a stack of paper plates and throw them.
Ready meals and takeaways for a few weeks will not do you or the children long term harm.