What is wrong in my wardrobe or how I can fix following problem I have with some of my backdrop pics and items: when I want to choose them for my outfit, they appear in front of my avatar, so my avatar is hidden behind it. Why does this happen with items under the backdrop layer option and what can I do, so they appear behind my avatar? I am clueless about it right now.

You'll need to drag the backdrop below your avatar base in the worn items.

Oh yes, now I know. Thank you :)

The reason some older backdrop-layered wears have a hole cut out of them is because it didn't used to be possible to cover over the base HA.