Is it really worth it to give 11M for an artifact?
And in the end do you get only 1?
Cause this amount of is way to much and its hard to acquire again at this point

Maybe later wrhn I capture a 100+ territory it will be easier.

What items are found and what's there value

A artifact gives a bonus that you keep forever(even on your next levels). so if you finish later in the level it's not that big of a deal.

Do you have to stay on a map in order to get the dig reward? I'm ready to finish a map, but still have 17 hours left on the dig site. Can I complete the map and still get the artifact? Or do I need to wait until the dig is done?

To answer both questions, you can dig for the artifact at the end of the level, when the costs are relatively low. The artifact dig progress is shown at the advancements section, this means you can start digging and then start another level without losing it, the digging will continue. If you have more dig sites at a level, I advice to not complete it until you have started digging at the last one

Does the clock tick only during idle time?

Nope, it is real time clock. Even if you go offline for 20 hours, it will count all 20 hours.