Fire Emblem has been very different with its dragons depending on the
setting, and even the same settings can have different kinds of dragon. The two or three big features are these: human form acts as something of a stabilizer for dragons who will eventually degenerate into beasts otherwise, dragons can live for a very very long time, and they are powerful as dragons but less so in human form.
FE1 and 3 take place in Archanea, which had a dragon civilization prior to the rise of humanity for at least 3,000 years. Something about their long lives and their magic led to infertility and sickness of both body and mind. They discovered the way to stop this was to take human form. One tribe disagreed: the Earth Dragons, led by their prince Medeus (yes, the one who recently showed up in FE Heroes), including a dragon known as Loptous (who becomes more relevant in FE4, but that's another story and we'll get there). Within 3 centuries, the earth dragons degenerated into monstrous beasts without a flicker of reason behind their eyes, leading to their attacking the fledgling human race. Naga and the divine dragons fought them. This ended with both the earth dragons and the divine dragons mostly wiped out through the use of artifacts made from Naga's fangs. The earth dragons were sealed and left in the care of Medeus. He got upset about how Manakete in their humanoid forms were getting mistreated and, well...how far he went and what he did is the plot of those games.
FE Awakening takes place a few thousand years later on that continent and eventually Manakete became rare and shrouded in myth.
In FE 4/5, Loptous made a blood pact with a bishop from Jugdral, binding most of his power to a dark magic tome, eventually possessing the bishop and forming the Loptyrian Empire. They crushed all resistance and ruled for 17 generations until a group of heroes arose to try to liberate the people. They fought for 20 years. Eventually the pleas of the crusaders reached Naga and 11 other dragons who formed pacts with heroes. These dragons gave the heroes weapons with a dragonstone inlaid as a means of giving them the power to turn the tide.
In FE 6/7, there was a time when dragons and humans lived in harmony. Everything changed when the Human Nation attacked, resulting in the Scouring, a war where humans sought to purge dragons. The dragons responded by forming a Demon Dragon to generate empty-husk "War Dragons", leading the humans to counter by forming legendary weapons so strong with magic they distorted reality such that dragons had to take on human form. The vast majority of dragons fled at that time. A few fled to an enclave of peace. One sought vengeance. The result is the plot of FE 7 and FE 6.
FE 8 has only two dragons we ever meet, Myrrh and her dad. Reanimated dragon corpses suggest there used to be more.
FE 9 / 10 has dragon laguz, one of a few different tribes of shapeshifters, who are bound by the rule of their king to a policy of isolation and neutrality in pursuit of a "peace" defined as the absence of outright war.
FE 2 / Echoes has two divine dragons in the roles of gods of neighboring lands. They are, unfortunately, starting to degenerate, leading to a certain degree of insanity and negative effects on their lands and the people within them.
3 Houses has the Nabateans in their varying degrees of sanity, ability to become dragons, and friendliness towards humanity.
Conclusions:
Dragons can live a long time, always.
Dragons are stronger as dragons than in human form, always.
Dragons need to go into human form to avoid risking "degeneration" into a mindless and aggressive beast.