What does a Dragonborn look like from a child to a fully grown adult. Specifically, how does their appearance change as they grow and mature, What clothing do they wear? Are they custom fitted or do they wear clothing made for human children? and are there any images of a dragonborn child.
There is, to the best of my knowledge (which is extensive but not totally comprehensive), exactly
one image of a non-adult dragonborn. Here it is:
The teacher is implicitly an older dragonborn, likely past middle age, which can be detected from subtle differences in the facial design--bags and crows' feet around the eyes, wrinkles at the corner of the mouth, long facial "hair," etc.
There's also another
unofficial image floating around that is not official, but which I quite like, and shows a very young dragonborn. Here's
a link to the original DeviantArt page. Entitled, "Rawr, I'm a warrior." by Igliang, in case the DA link ever dies. (I would show the image directly, but DA links are
horrible link gore.) As you'll see below, this child is likely only 3-4 years old.
However, while we don't have much in the way of
images, text from 4e actually tells us quite a bit about the way dragonborn develop! Here's a (relatively...) quick summary.
- Dragonborn lay eggs, but also suckle their young, similar to monotremes. It's not clear exactly how long dragonborn children gestate inside the egg, but it's not a short period, likely at least a couple months.
- Within hours of hatching, dragonborn children are able to walk. Their teeth require a few months to come in, during which time they nurse; the mother transitions her child(ren) slowly to soft food, then hard food. (This usually contains a higher proportion of meat than is typical of other humanoid races--implicitly, dragonborn need more protein to support their physiology and development.)
- By the end of their first year of life, a dragonborn child has reached the mental and physical development of a three-year-old human.
- They mature quickly. By roughly age 12, a dragoborn child "is a lanky version of his or her adult self." This means that dragonborn finish their growth spurt around the time humans start theirs. (Thus, the dragonborn youth shown in the official picture above is somewhere around 12-14.)
- It takes about three years from the end of their puberty for a dragonborn to reach full physical and mental maturity.
As a result of the above, dragonborn mature extremely quickly compared to humans. They have essentially nothing equivalent to "infancy" as we understand it, and their "childhood" phase progresses more quickly (only 6-8 years as opposed to the 9-12 years for most humans, depending on sex, genetics, and nutrition.) The child in the unofficial image I linked could theoretically be as young as two years old, but 3-4 seems more reasonable given the child's physical coordination.
Edit: To answer some of your other questions, at least to the best of my ability (noting that much of this is speculative)...
How does their appearance change from hatching to adulthood?
The implication of the bit about how a dragonborn is "a lanky version of his or her adult self" (from
Ecology of the Dragonborn and, IIRC, also
Player's Handbook Races: Dragonborn, both 4e materials) is that before that point, dragonborn children do look like children and not like small adults. Thus, we can assume that, other than essentially skipping the infancy stage, dragonborn children have loosely similar proportions to humans: more slender, slightly oversized head for the rest of the body, facial features more clustered near the "bottom" of the face (which will grow down and outward as the child ages), limbs that are short compared to torso/head and which elongate as the child grows, etc. However, given that dragonborn apparently need to eat more protein than humans, it's possible that even in childhood they are more muscular than a human of similar developmental age (meaning, accounting for stuff like "dragonborn at 1 year old are equivalent to a 3 year old human.")
What clothing to dragonborn children wear?
There is no special information, but if this were something physiologically distinct, one would think one of the works mentioned above would say something about it. Since they don't, it's perfectly reasonable to say that dragonborn do the same things humans would in any given setting. Most likely, affluent dragonborn would pay for their children to have truly tailored outfits, while poorer ones would use hand-me-downs and generic child-shaped clothing (or wear adult clothing with belts and the like.) Since they mature very quickly, however, it's possible that they put more of an emphasis on looser/flexible clothing that can be adapted to suit. That way, they don't have to buy clothing quite as often.
Hopefully that is helpful!