About how long in earth time did it take for the children to come after they heard Tirian’s call for help?  How long was it in Narnian before they arrived?   

It took them a week to prepare to come back Narnia and this is the earth time.

But in Narnia, Tirian’s dream led him into the children’s world just ten minutes ago, so it was only 10 minutes after Tirian woke up, the children appeared in front of him.  

About how long had Rilian been dead since the children were last in Narnia?   How did the children think they would get into Narnia?  Why didn’t that work? 

Rilian had been dead over two hundred years since the children were last in Narnia. And Tirian was the seventh in descent from Rilian.

The children thought they could get into Narnia by using the magic rings.  but it didn’t succeed because they appeared in Narnia suddenly without seeing or touching the rings. It might be that Aslan did all for them in his way without any Rings.