My experience base is with larger parrots so I also contacted a club member that specializes in the smaller psittacines to confirm my advice and learn more.

First of all we are entering Spring and the days are lengthening. Most of us are starting to see changes in the behavior of our birds. My guys are just starting to molt some of their contour feathers. In budgerigars (AKA budgies or commonly, parakeets) this is the time they will show interest in nesting behavior and reproductive hormones may run high, hence the egg laying. Your birds are of the right age to become sexually mature. Sometimes the presence of another bird close by (cagemate) can help in triggering the egg laying process (even though the other bird is also a female), but the drive to protect the eggs will set the one that is laying the eggs against the other. The attention to the "bird in the mirror" is also related to this protective drive so you may want to remove the mirror for now.

You MUST SEPARATE the two females before you have a serious injury or death of one of your birds. You will need another cage similar to the one you are using now or adequate to housing just one bird. You can place the cage in close proximity so they are still aware of each other, but you NEED to give them each their own space. This will not always be true, but for this season and with this current situation they need to be apart from one another now.

Even though you are not providing a nest box she will attempt to "nest" in other ways, tearing up newspaper that she can reach at the bottom of the cage, tearing parts from an available toy, even digging in the food dish (you may want to try a different kind of food container that is not as large if she is trying to get in it). Try to limit her access to those nest making materials as these activities pop up (don't strip normal toys from the cage, the general environment can remain the same). Leave the eggs she lays where she gathers them on the cage bottom. She probably will not sit on them but if she does there is no harm and that activity will preclude her from laying more. If you remove the eggs she will continue to lay more and the danger is in having one not exit normally from her body, called becoming "egg bound". This condition is very serious and death is likely without a visit to an avian vet. Leave the eggs for two to three weeks (normal hatching time is about 17-21 days) unless you are convinced that she is not paying any attention to them at all. But, initially they need to stay to stop the egg laying process. After they do not hatch she will lose interest and may break them herself and you can remove them.

The male budgie has a blue cere and sometimes it may just appear as a blue line or border so look carefully - that may help you in figuring out the sex of the other bird. The crusty cere can be something simple or may be indicative of other health problems. First, simply let this bird bathe a couple of times in close succession over a couple of days and see if that helps. We don't often realize how often they need to bathe and if not given access to water in a dish (pie plate, etc) or gently sprayed or misted regularly they can have some difficulty clearing dust from their nares. Being through a cold spell recently the relative humidity of our homes has been very low unless you are using a humidifier or attending to it in other ways. Dry air can cause respiratory problems and this may just be the result of the dry environment we have had indoors recently.  My resource person mentioned the importance of a cuttlebone for self grooming of the beak and face and also perhaps to scape some of it into the water bowl to increase calcium intake somewhat. Egg laying can be very taxing nutritionally on a bird (creating the egg and shell not to mention the molting of feathers this time of year) so be sure you are giving your birds a good diet.

Please feel free to contact me through the club website if you want to be referred to someone to mentor you in the process of working through this situation or in caring for your birds in general. Also I would be interested to know how this all works out for you and your birds and to expand my own knowledge. Contact me through this page.