But I can't really understand how I can do this with a visual software.
Hi… this is kind of a broad question, so I'll try to break it down a little so you can start looking for your answers.
Most of of what you describe is a 'character controller' for Unity. There are many 3rd-party available, but also some provided by Unity (I believe there is a 2D character Controller in Unity's default 2D platform example (the one with the UFO). This will actually cover most of your needs and it's a great place to start. (some controllers are 2D sprite-based, some are 3D figure-based).
You can do the basic setup without coding or Playmaker, and there are tons of tutorials (without Playmaker) for very beginners. You'll want to watch/learn the basic concepts before trying to make your own. Things like running to the left/right, jumping, etc are built-in
Playmaker isn't exactly visual coding, it's a function state machine… very like your description of setting up a state, reading inputs, and transitioning to a new state.
Getting started, once you understand the basics of Unity's systems, Playmaker will allow you to take control of those systems, spawn enemies, create simple behaviors and AI with states: "detect when player is near, and switch to attack-mode" for instance.
I recommend looking at a few of Unity's official tutorials to get the basic concepts (how Unity calls everything) and then search for PM tutorials – I found several but you will know the kind of tutorial you need once you understand some of Unity's terminology (and there are quite a few)