will the mother budgie be able to feed her offspring by herself?

yes, usually both the mother and father budgies will feed and take care of em.

check dis out. http://www.budgieplace.com/breeding.html

The mother budgie will lay eggs in the nest-do not go near it or she will become territorial and bite off your fingers (maybe). Leave her be, and make doubly sure there is fresh food and water always available. Her mate may also help her. Once you hear cheeps of chicks, be sure to still stay away from the nest itself, and put some treats in, maybe special ones for the momma. She will feed them herself. When they are old enough, they will come out of the nest. Once they come out of the nest, the mom will help them if needed, but they will most likely be able to feed themselves at this point. Still leave the nest alone, as it may be sentimental to the chicks. When they are big, you can begin to train them. If the mother fights one of the chicks alot, then it is time to separate the mother and chicks, as the mother may fight the other females when they get old enough.

yes