Just to add a few things. The reason why Kes was captured by the Kazon was because she managed to find a way up to the surface where the Kazon found her and captured her.
As for her stay with the Kazon, I think she was only there a few weeks, otherwise they would have forced her to tell them how to find the tunnels (even if she probably didn't know it, she was looking for the way back to the tunnel when the Kazon found her).
As for Kes's birthday, it is celebrated somewhere between the episode "Elogium" which takes place at Stardate 48921.3 (Friday 3rd December) and the episode "The 37's which takes place at Stardate 48975 (Wednesday 22 December). My suggestion is 17th December.
Assuming that Kes's birthday is in December and the episode "Caretaker" takes place at Stardate 48315.6 (Monday 26 April) we can assume that Kes's father Benaren died and Kes left the city somewhere between the middle of December 2370 and 26 April 2371.
According to the book "Pathways" by Jeri Taylor, Kes's father died one month before she went to the surface. According to the same source, she had been prisoner at the Kazon camp for five weeks before Neelix showed up there. Two weeks later, the Kazon discovered that Neelix stole water and chased him away and two days later, the Voyager crew arrived.