It is unclear.
However, the text of Astral Projection and the Astral Plane seem to indicate that you can.
The Astral Projection spell states:
Your astral form can freely travel through the Astral Plane and can
pass through portals there leading to any other plane. If you enter a
new plane or return to the plane you were on when casting this spell,
your body and possessions are transported along the silver cord,
allowing you to re-enter your body as you enter the new plane. Your
astral form is a separate incarnation. Any damage or other effects
that apply to it have no effect on your physical body, nor do they
persist when you return to it.
From Creating a Multiverse -> Astral Plane -> Astral Projection (Dungeon Master's Guide page 47)
Traveling through the Astral Plane by means of the astral projection spell involves projecting one's consciousness there, usually in
search of a gateway to an Outer Plane to visit. Since the Outer
Planes are as much spiritual states of being as they are physical
places, this allows a character to manifest in an Outer Plane as if
he or she had physically traveled there, but as in a dream...
A character's death-either in the Astral Plane or on the destination
plane-causes no actual harm. Only the severing of a character's silver
cord while on the Astral Plane (or the death of his or her helpless
physical body on the Material Plane) can result in the character's
true death.
These would seem to indicate that you at least can choose to remain in astral body form, so long as your body is somewhere other than the material plane.
To address the questions added since first answering, I will add the following:
1- Yes
Your astral form is a separate incarnation. Any damage or other
effects that apply to it have no effect on your physical body, nor do
they persist when you return to it.
2- Yes
The material body you leave behind is unconscious and in a state of
suspended animation, it doesn't need food or air and doesn't age.
Plus, you would not age at all while this spell is in effect.
From the Dungeon Master's Guide section on the Astral Plane:
Creatures on the Astral Plane don't age or suffer from hunger or
thirst. For this reason, humanoids that live on the Astral Plane (such
as the githyanki) establish outposts on other planes, often the
Material Plane, so their children can grow to maturity.
3- Yes; as long as your cord is intact
If a creature's original body or its astral form drops to 0 hit
points, the spell ends for that creature. If the spell ends and the
silver cord is intact, the cord pulls the creature's astral form back
to its body, ending its state of suspended animation.
4- Too fringe to rule, Ask Your DM
Personally, it seems reasonable to me, for the most part. The question is, what about when you attempt to have your astral body re-merge with your physical body? Thus the requirement of DM ruling.
Dragons change their physical characteristics, but not their cognitive capabilities.
Ancient Copper Dragons have the ability to change their shape (MM 110 edited for clarity) Dragons in general (MM 84-118) only gain the ability to change shape at the age category (MM 86) adult or ancient depending on their colour:
Change Shape. The dragon magically polymorphs into a humanoid [...]
In a new form, the dragon retains its alignment, hit points, Hit Dice,
ability to speak, proficiencies, Legendary Resistance, lair actions,
and Intelligence, Wisdom, and Charisma scores, as well as this action.
Its statistics and capabilities are otherwise [!] replaced by those of the
new form
The physical age appearances of the new body are not tied to the shapechanger, but the shapechanger retains their cognitive capabilities. To be a dragon capable of Change Shape this preassumes an age of 101+ years, so the character is always an adult by the book and well suited to marry an elf that assumes adulthood at around 100 years (PHB 29).
If you decide to give the Young Copper Dragon (MM 111) the ability to Change Shape, then this would be a marriage between entities which are considered not adult but would both have a physically mature body (PHB 23, 29), if the dragon chooses to assume the shape of a physically mature body. As to say it would be two non-adults marrying each other by political necessity.
There is no by the book basis that makes Dragon life stages comparable to human social categories like a toddler, pre-schooler, child, etc. By the book, dragons do not adhere to these categories.
You are the DM and can make it up as you see fit. If you want to get some inspiration (including player character dragons), then you might want to read Draconomicon: The Book of Dragons which is for 3e and 3.5e
Best Answer
From a rules perspective: no
While this isn’t stated anywhere explicitly, we can infer it in the fifth edition from the rules for Monsters.
Of note, only adult or ancient metallic and gem dragons have the Change Shape ability, so most dragons capable of using it are already in the older age categories. This makes it a non-starter for the purposes of aging out of the less powerful younger categories.
The rules for the Change Shape ability - and for similar ones used by other creatures, and indeed for spells like polymorph etc - tell us what does and does not change for a dragon or other creature who uses it. Here’s the relevant second paragraph of the ability used in the stat blocks for ancient metallic dragons in the Monster Manual:
The changes are thus limited to those noted in the stat block of the new form, with the exceptions stated. Lifespan and a “rate of aging” are not features of stat blocks, and are not noted at all for most beasts. Most humanoid stat blocks leave open the question of which race they belong to, meaning that how they age is explicitly not part of the stat block, since different humanoid races can have very different lifespans and rates of aging.
From a lore perspective: also probably no
This is also not stated anywhere explicitly, but in the write-up for metallic dragons it mentions that some choose to spend considerable time in humanoid form to immerse themselves in other cultures. There’s no mention of this affecting how they age, which would be a significant limitation on this behaviour, so it seems unlikely to be the case. There is also at least one example of a long-time disguised dragon in a published adventure which makes no mention of any such problem with aging (I’m not being explicit about this one as it might be considered a spoiler).
The closest to an official lore answer appears in Fizban’s Treasury of Dragons, where at the end of the section on shape changing it mentions that some dragons believe if they spend too long in another form they may be trapped in it:
This suggests they wouldn’t age and die as a human or beast would, but live out their normal dragon lifespan of centuries.