Hi Yuki!
The olive oil isn't the same as vinegar in the chicken's nutrition.  Look in your kitchen cupboard....most houses have vinegar, and if you don't have any, then ask your mother to pick up a bottle next time she is in the grocery!!! Vinegar is pretty cheap.  The reason it helps them absorb calcium is because it is acidic.
Here is a 'science experiment'
https://www.google.com/search?q=soa.....69i57j0l5.5580j0j7&sourceid=chrome&ie=UTF-8
Perhaps you could combine your chicken raising with your school work?  Your mother is right that chickens shouldn't need other than pellets and plenty of water.  Maybe you could talk to her about how this is important to you, and ask her for her help in taking the best care of your chicken and explaining that it is a pet, as well as livestock, and that you will be learning new things while trying your care process.
A smallish bottle of apple cider vinegar is pretty low cost.  Put 1 Tablespoon in a gallon of water....and let your flock drink from that.  If you cannot purchse oystershells, then be sure to give the shells from the eggs you use back to your chickens.
You can dry them out by just letting them sit for awhile.  I put mine in the microwave oven on a paper plate for about 1 minute 30 seconds -- and they are easy to smash with a can -- and then I roll the can over the paper plate to make the shell pieces small.
Good luck with your chicken -- hope you can get hold of some vinegar and you can feed eggshells to your flock!

ETA - if you are not able to get vinegar, send me a PM, I might have an idea that would work for you.  Remember too, that chickens do have a time when their egg laying days are over, and when their life ends as sad as that makes us feel.