Please note: Much of this information does not apply to Brotherhood.
The order of episodes goes something like this:
- Episode 1 flashback
- Episode 28 flashbacks
- Initial alchemy training under Izumi
- Pre-automail for Edward
- Episodes 3 through 9
- Barry the Chopper
- Shou Tucker and Nina
- Episodes 1, 2, and 10 through 51 (not counting flashbacks)
- The Conqueror of Shamballa
I have missed a few brief flashbacks here, but this is the general idea. You can use Edward's age, somewhat, as a marker of time passing. He is ~11 in the flashbacks of their mother, 12 during his State Alchemist qualification, and turns 15 prior to the main story (the incident in Lior, etc.). He is 18 during The Conqueror of Shamballa. (This is shown by 14-year-old Al reverting to being 10 years old, then aging to 13 when Eckhart starts breaking into Amestris. Since he is one year younger, and would be 17, Ed is about 18.)
Here is a handy chart for a full comprehensive view of the series (click to enlarge, or click here for the spreadsheet). Note that Edward does have a birthday in the main timeline, when he turns 16.
(Orange = pre-anime; yellow = flashbacks; green = anime series; blue = post-anime)
To address your point about Ed's appearance: Edward doesn't actually look the same at 12 as he does at 15. At 12, his eyes are slightly larger and his face is a bit rounder, save for his chin, giving him an overall slightly younger and more innocent look. It's not generally noticeable in the more zoomed-out shots, but it's there. (Also remember that, to perpetuate the "shorty"/"chibi" jokes, he couldn't grow much, so all the changes are facially.)
(Left: 12-year-old Ed, episode 4, 6:45; Right: 15-year-old Ed, episode 10, 13:50)