Aren't dragons immortal until you absorb their souls? How did the Blades manage to fight dragons then? I'm pretty sure they couldn't absorb dragon souls.

The Blades of those days used Mages and Archers to hunt them down. They were killed, but not permanently killed. Only a Dragonborn can permanently kill a Dragon.

So when they were killed, how long did they stay killed?

^^ What he said^^ Also you are talking about the Akaviri Dragonguard though there is some evidence that the Blades might have hunted dragons for a while after giving their allegience to Reman.

They bend over and let the dragons bite them in the backside. thats how the blades roll.

For possibly thousands of years. As Arnathorn said, they were known as the Dragonguard back in the day.

Is it possible for them to awaken any earlier? Or is a couple thousand years a general time span until they reawaken?

As far as we know, only Alduin can revive them. They can't permanently die if they still have their soul intact.

As ShadowTitan said the bodies of the dragons may be killed but unless their soul is absorbed by a dragonborn they can be revived. Only by Alduin to our understanding or according to lore though there are some who champion otherwise.

The dragons that die after Alduin is defeated will remain dead until Alduin returns to do the job he was created for which is to end the kalpa which in layman's terms is to end existence as it is known now and reset the 'clock' on Nirn, returning it to its beginning and start the process all over.

You do realize that the body can be killed but the soul can not without another dragon or even dragonborn.

Alduin wasn't around to resurrect them. So they stayed "dead."