Are save games compatible between Deus Ex Human Revolution and the Director’s Cut version

Yes you can. I dropped a few things in the apartment the first time I dropped by. A few locations later and a trip back to Detroit and those items are still there.

Be mindful that you don't always have access to the apartment though.

The "Missing Link" DLC has been announced (for October), but this will apparently be set in the time between Jenson leaving Hengsha and arriving in Singapore so will not carry the story forward past the end of the game, but it may well provide more exposition on how the games are linked.

However, they have already made some fairly strong links between DE:HR and the original. Specifically, the little hidden element from the credits (that you mention) infers that Megan Reed is working with the Bob Page (and therefore the Illuminati), so is presumably using Adam's DNA to help them develop the nano-augmentations that appear in Deus Ex and the "nanite-virus chimera" mentioned may presumably result in the Grey Death.

There are also other weaker links throughout the game, for example when Jenson detonates the bomb in Hengsha shipyard he inadvertently allows Tracer Tong (a major character in Deus Ex) to escape the island. There are others too, I'm sure, but I won't try to list them all here.

A few of the Wikia pages provide more in-depth information, here's a few that are the most pertinent:

Deus Ex: Human Revolution, Plot
Adam Jenson, 2027
JC Denton, Early Life
Nano-augmentation, The beginnings