Well, Bill, is the big problem in Spanish :-)
But: in the first sentence "Salí y estaba lloviendo".
"Salir" is just one time, one moment, and the rain lasts longer, is "durability" for more time. So, you need imperfect in "estar lloviendo". in adition, is the description of the situation. (Normally, we don´t say "salir afuera", only "salir", because is a redundance; and the weather verbs are always written in singular).
The second sentence "Me subí a un árbol y me caí" o "Cuando me subía a un árbol, me caí". You can to say both, but means something a bit different.
"Me subí a un árbol y me caí": you climb the tree and then you fell. One time, completed actions.
"Cuando me subía a un árbol, me caí". While you were going up (duration), you fell. You could not go as far as you want. Only the second action is completed ;-)
I hope this was a little help to understand the pasts.