Content structure:

You did mention the lack of structure, among many other arguments. In your fixes, you made a good attemp to group items into categories. " I don't quite understand what you mean by "In this web site, the user cannot follow an order to fill the different fields. It would not be easy if the user wants to do all the steps, for example: identification, visiting the index of contents, following the some searcher." The search panel is well structured. I don't think there is anything wrong with it.

Layout design:

You didn't mention the problem of proximity.

Visual consistency:

You didn't mention any of the visual inconsistency problems: the alignment problem and the fact that images were used randomly and the lists were rendered differently. In your re-design, there are two many lines in the search panel. The lists have visual inconsistency.