[quote=@Metamore]
[@Balthazar007]
Let's say Rin [i]does[/i] decide to fight this Chikorita, how exactly would that go? I know it says you'll roll two dice, but I don't understand what you mean by the die will represent their level, or how typing would come into play. 
Could you give an example?
[/quote]

So!

Totodile is Level 6. 
Chikorita is level 15. 
Chikorita has one type advantage (Grass over Water). So she will get a 50% boost (50% of her current level 15). That equals a 7.5 boost. I always round in the player's favor, so that means she gets a 7 point boost. Totaling 22 points. 
I now roll a level 6 dice (your Totodile) and subtract a level 22 dice roll (Chikorita). 
Here is a sample result:
https://www.roleplayerguild.com/rolls/4679

As you can see, that is a -12 result. Meaning that Chikorita rolled a number 12 points higher than your Totodile rolled (in this example). Your Totodile thus takes 12 damage (more than what she can handle) and faints.

If you would have lost by less than 6 points, health would have went down, but you could have kept battling. Even with less "health" you would still roll a die 6 in battle. 

If you would have won the dice roll, the Chikorita would have lost health instead, but you probably wouldn't feint him. Best case scenario, Totododile rolls a 6, Chikorita rolls a 1, and Chikorita takes 5 damage. You can then keep battling or try to catch the Chikorita with one of your Pokeballs. 

A Pokeball dice roll is similar to a wild Pokemon battle. Pokeballs have a level 7 catch rate. 
This means I will roll a die seven and subtract a die 15. 
If the result is positive (meaning that your roll was higher), you will catch the Pokemon. If it is negative, the Pokemon [u][b]may[/b][/u] run away. If you battled the Pokemon first and weakened it, the level seven dice will be rolled against the Pokemon's lowered health stat. 

The run away function is determined by a background dice roll. i.e. a more complicated spread sheet random number generator.

I hope I didn't overload you two with all that information. Let me know if you have anymore questions though.