how the catch system work?
Answer: the first Pokemon you see in a route is your encounter. So if you go to route 1 and the first thing you see is rattata then catch that rattata. If that rattata run away/fled before you even could interact with it you cant catch anymore Pokemon there
how to level up Pokemon?
Answer: trainer battles and catching Pokemon. Let me explain about the "catching Pokemon", so you just catch Pokemon to level up, but you obviously cant use it(its so obvious). Just make a mark for the Pokemon you used for grinding and make another mark for the dead Pokemon
Edit: like fizz said, its your nuzlocke and your own rules. My answer is based from youtube and my rules
Source: youtube videos I watch and my brain
Hope I helped!