It sounds to me like they are all going to be fine...If you've never done this before or aren't familiar with the process of the parents feeding them, then it's completely normal to worry about them, and I'm glad that you did. When the parents feed their babies, they never feed them all right in a row, because they are all at least a day or two apart in age, they all have different food quantity requirements, they all empty their crops at different rates, etc. And it's also not unusual to see the chicks actually "beg" for a feeding at completely different times throughout the day from their siblings. It's really common to hear one chick in a clutch crying for food, and then when you look in the nest-box, every other chick has a full or semi-full crop, and the chick that is crying has a completely empty crop. So that's totally normal and fine...
At 5 weeks old they should start abundance-weaning now. The parents will pretty much take care of this and you'll not need to do a whole lot, but I would make certain that all of the chicks have easy-access to whatever staple food you want them to wean onto,
hopefully that is a high-quality pellet! It's great to start-out the weaning process with millet sprays, and once you see that the chicks are completely devouring an entire millet spray, which should happen in a day or two at 5 weeks old, that means that they already know how to "shell" and eat seeds, which is a pretty innate ability anyway...
However, the unfortunate reason why most parrots won't eat pellets and are difficult to convert onto pellets is because their breeders don't wean them onto pellets from day 1...and your chick's "day 1" is right now. So I'd give them a millet spray, you can put that right in the nest-box with them, and make sure it disappears....but please, even if you don't feed your adult parrots a pellet staple, please go a purchase a high-quality, NATURAL pellet (NO FRUIT PELLETS! They are loaded with sugar that turns into fat and is stored in their livers!), and put a dish of them in a spot where all of the chicks have access to them. I don't know if you feed your adult birds pellets, if you do that's great, but I have no idea...If not, please get these guys weaned onto them starting today, and keep in-mind that sometimes you need to even soak them in some fruit-juice to soften them at first, so they'll eat them. Some great brands of NATURAL parrot pellets are Harrison's, Tops, Zupreem Natural, and Tropican. Make sure that you get the smallest size of pellet for them, which will not be the size of pellet that is made for their species; each of the pellet brands I listed above not only makes Natural pellets, but they all make their Natural Pellets in a size for American Budgies/Parakeets, and that's what you'll need for your chicks until they grow in size. After they are fully-weaned onto the smaller Budgie/Parakeet pellets, then you can just buy the same brand/type of Natural pellets, but in the Conure size. For now though they need to be small.
As far as what to do when/if your female lays eggs again, which she probably will, especially if she is housed with your male, you need to remove each egg immediately after it's laid, and either boil it for 20 minutes and put it back in the cage, or you can buy fake-eggs and just swap each real egg out for a fake egg, and destroy/dispose of each real egg...Either way, the next time you find an egg inside of the cage anywhere, do not provide her with a nest-box again, nor any type of "nest" at all, nor any nesting material, such as bedding, wood chips, fabric, etc. NOTHING! All you need to do as soon as you find an egg is to remove it and boil it immediately/use a fake egg, and put the boiled-egg or the fake egg on the bottom of the cage, right on the grate. No nests, boxes, not even a towel or a blanket. Any nesting material/boxes, any type of nest or anything that will make her more comfortable or provide the eggs with protection will only serve to trigger her hormones and the more eggs she'll lay, plus she'll not lose interest in them nearly as quickly if they are in a box or on a nest or soft material...So just boil the egg and put it right back in the cage on the floor/grate, and simply do the same with each future egg in the clutch...Without any nest/box or nesting material, she should lose interest in laying on them very quickly after she realizes they aren't going to hatch, and as soon as she stops laying on them and you're certain she's not paying them any attention, then simply throw them out...any eggs that break, throw them right out...****And keep in-mind that she will lay eggs a day or two apart, and that the mother will typically not start laying on any of the eggs until there are at least 2 eggs laid, often times they wait for 3 eggs to be laid. So just let the newly-boiled first or first and second eggs lay on the grate of the cage and just wait, don't throw them out if you don't see her laying on them, as she will lay on them after she feels she has laid enough to start...If you throw the first egg or two out because she isn't laying on them and you mistakenly think that she's already lost interest in them, she'll only kick it into high-gear and immediately start laying more eggs, probably more than she would have originally.
