Welcome to the forums,
I'm very sorry for the whole situation with your budgie couple and the multiple clutches they had over the past year.
For overall health reasons, it's not advisable to allow budgies older than 4 years old to breed. At this point your pair (especially the female) must be quite debilitated and it's imperative that you take strict measures in order to discourage further breeding behaviour leading to more egg laying.
Your female's calcium levels must be quite depleted by now and that combined with her old age make her much more prone of becoming egg bound.
The link previously given to you should be very helpful in keeping your budgie's hormones under control.
I agree that at this time, it would be best to house your pair separately.
Be sure to not have any dark hiding areas nor anything that your female can potentially use as a nest and this includes open food bowls where she can sit on.
Regarding the weaning, it's extremely important for us to check the chicks' crops on a daily basis to see if they are filled with food.
By the end of the day (at sundown) they should have nicely filled crops
A nice and filled crop should be visible and we can also gently palpate the area by using the thumb and index finger. A full crop should feel hard to the touch when gently checking it.
Weighing the chicks on a daily basis and keeping track of their weight is also a good measure during this delicate time on the chicks' lives.
It's also our job during weaning to give an extra support to the chicks and help them out to try all the different types of food and actually encourage the chicks to eat them. This is incorporated in the bonding and socialization of the chicks when spending daily quality time with them.
Be sure to check this link for the detailed information: Planned Co-Parenting in Raising Tame Chicks
If you are ready to give up on pet birds and your heart is no longer with them, then screening potential new owners who are experienced with birds and are truly passionate
about them will be the best choice. And this is done by thinking of your flock's long term welfare and happiness.