Hey there, i have recently descovered that my original bird Gizmo is in actual fact a female

My grandmother passed away just before christmas and i decided to take in the family bird buzby who is a boy. They have shared a cage for quite some time now and got on well. I had gone to spain for a week to come back yesterday to find three little eggs and mother sitting on them (Gizmo) this was not a planned event as i was told both birds where male.... This is the first time to breeding birds and dont know what to do. I have tried to research about them but everything tells me different.
The mother laid the eggs on the bottom of the cage (i read that this should not be the case) however i also read that i should not touch or interfer with the eggs or the pair.
Can anyone give me advice on what i should do. I would love to breed these chicks to little spring cockatiels and would like it to be a success

. I think the eggs have been laid for aprx 2-5 days.
many thanks