Since there isn't a .blend file, it's going to be challenging for us to properly diagnose your solution, since we won't be able to reproduce your setup.
That being said, I can see one thing that might help. The "quality" counter that you show in your screenshots is at 1. When I simulate cloth, I often increase the quality steps. For example, in Blender 2.82a, if I make a plane and apply the cloth modifier, I usually use these quality steps:
I increased the Cloth -> Quality Steps from the default value of 5 to 10. Furthermore, I increased the Collisions -> Quality from the default value of 2 to 5, and turned on Collisions -> Self-Collisions. Since your screenshots show quality values of 1, you might want to significantly increase that number. I would recommend looking at some Blender 2.7x videos that use cloth, and pay close attention to the quality steps value that they use. For example, this video seems to use values of 5 for the quality steps.
As an aside, consider using Blender 2.8. The more recent versions of Blender have significant improvements to the cloth simulator. For example, consider this blog post or the release notes Wiki, which for example, say that 2.83 has improvements with cloth collisions.