Questions about pixel-style 2D platformer implementation

Unity Engine
1

I’ve just started learning unity and am trying to implement a simple 2D platformer for some practice.
And here’s 2 questions:

  1. How to set edge collider 2D precisely? I attached a edge collider 2D to the ground, and the character has a box collider2D component, but I can’t find a way to set the vertices’ position of edge collider precisely, so the character always seems to be floating several pixels above the ground, which bugs me a lot because that becomes way more serious when the target platform’s resolution is quite high - it looks like that the character floats “half pixel” or “quarter pixel” above the ground.
  2. How do I implement a platform that when the character jumps he can go through it but when he falls he lands on it, with unity’s 2d physics?
    Thank you for the reading.
2

One more question, how to judge whether a character is on the ground?
The tutorial I found on the website used a raycast, which is flawed because when the character stands on the edge of a platform, he’s not grounded - a case that is quite common for many platformer.
It’s quite confusing for me, the character lands on a edge collider2d, isn’t there a function to know which object it’s landing on? Why an additional ray collision test is needed? Did I miss something?
The tutorial: Unity Asset Store - The Best Assets for Game Making
Here’s when it go wrong:

3
  1. = this post
  2. I saw several posts addressing this functionality here and in answers. Check around - you will find it.
  3. This is addressed in several posts also.

Good luck. Post a picture of your character.