Character stucks always (Rigidbody/Character)

Hello there,

i am working on a 2D-Platformer-Game and i am struggling with the Physics of the game.

So, we built the level with the cool "Uni2D"-PlugIn and gave the plattforms convex physics with the PlugIn-Feature, and set the "Edge Simplicity" to 1, so the collider is kind of "pixel-by-pixel".

The Problem is the Main Character. I really tried to, but i didn't manage to work it out with Character Controllers or Rigidbodys, here is the thing ( i made some poorly drawn pics):

Think of it as the first plattform, and think that the whole plattform is a collider.

So, here is the character, and i managed to move him quite well around on the ground. BUT:

When i jump, the Character is stuck at the Cliff/Corner, then, i have to jump again, and sometimes, i just press to the right and he kind of flies away. This is the behaviour with an Character Controller.

I also tried to do it with a Rigidbody + BoxCollider/SphereCollider/CapsuleCollider. Nearly same results, but the BoxCollider is the worst, it just goes THROUGH the ground.

Here is the script i used (for the CharController-Version):

 using UnityEngine;
 using System.Collections;
  
  
 public class charControllerMovement : MonoBehaviour {
  
     public float speed = 10.0f;
     public float jumpForce = 10.0f;
     public float gravityForce = 20.0f;
     public CharacterController controller;
     //the direction we are going to move
     private Vector3 dir;
  
     void Start()
     {
         //load a reference to our character controller component
         controller = GetComponent<CharacterController>();
     }
  
     void FixedUpdate () {
  
         //is the user pressing left or right on the keyboard?
         dir = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
  
         //transform direction to local space
         dir = transform.TransformDirection(dir) * speed;
  
         //apply gravity
         dir.y = controller.velocity.y - gravityForce * Time.deltaTime;
  
         //are we jumping?
         if (Input.GetKey("space"))
         {
             dir.y = jumpForce * gravityForce * Time.deltaTime;      
         }
  
  
         //move our character
         controller.Move(dir * Time.deltaTime);
  
  
     }
  
  
 }

I really don't know how to handle this behavior, and would be really really grateful if someone could give at least a hint how i could manage that.