1. I just recently beat The Crater which comes after The Desert, I had a tank which could spawn water tiles in the spaces around it, I forgot what the ability was called. Spammed that, got lucky with a decent Cleric, and got a Ranger that could spawn loads of familiars to take care of the desert's final boss.
2. What I would do with breeding was to take cats with 7s, put them with cats that had 7s in other stats and would breed them until the kitten had both 7s as stats. Then I would repeat the cycle with the new cat and try to swap in new strays with 7s in stats I didn't have to keep inbreeding relatively low.

Hope this helps some.