Need advice on hand-rearing baby budgies

[Dilligaf]

My brother's budgies recently had babies. Unfortunately something managed to take/kill the parents when the 2 babies were about 1 week old, even though the cage had a layer of chicken wire all around it. Due to his work schedule, my brother couldn't commit to raising the babies himself, so I took them as there's always someone home in my house. We don't really know what we're doing other than the basics: feed them and keep them warm and clean. I've asked for advice at a few different pet shops but none of them really have a clue. So I have quite a few questions that I'm hoping someone can answer.

We think they're about 5-6 weeks old now, but there's a huge difference between the two - photos below. The smaller one is only 1 day younger but it's really underdeveloped compared to the big one. It was half the size of the big one at 1 week old when I got them off my brother. That being said, it has grown more in the past week than it did during the first 4-5 weeks. Its feathers are coming through now but about 2-3 weeks ago it had flaky skin and no one at the pet shop knew what the cause of that was. I haven't had any issues with feeding it. The bigger one is quite well feathered and starting to use its wings now. It can fly over 1 foot directly up and can go between sticks and perch.

So my questions are:
1. Why is the smaller baby so far behind in terms of development?
2. How do I go about weaning the bigger one? What do I feed it, how often etc.
3. Should the big one be spending more time in its small cage so it can get better at flying/perching etc. rather than in the shoe box with the little one? The little one seems to want to huddle quite a bit still even when it's warm, so I'm not sure how it would cope if I left it alone during the day while the big one is in the cage.
4. Are there any other tips or info I should know? If it wasn't obvious, I've never done this before and don't really know what I'm doing most of the time.