What's the actual problem? Zotero shows embedded annotations like any other PDF reader. If you want those to be editable, go to File → Import Annotations to transfer them from the PDF file into Zotero itself, where they'll be editable.

I need Zotero to show only annotations (notes, nor highlithing) done with Zotero as Mendeley does

I want to keep my previous work. What I dont want is my highlightings to be considered among Zotero notes. I dont want 106 notes listed for every Underlining and highlighting previously done on Adobe. I dont understand what are you suggesting: File + import and then? See my screenshot
https://s3.amazonaws.com/zotero.org/images/forums/u17619333/a61g1gaihq9kl9hfygal.png

Ok I try

Ok. Sorry. Done. Now?

I think you may be misunderstanding something here. Your screenshot shows the Annotations section of the item pane. The whole point is to show you the annotations you've made on the PDF — which includes highlights, underlines, note annotations, ink annotations, etc. That's going to show annotations you made in Zotero as well as other PDF readers, because they're all annotations. It would make no sense to show highlights created in Zotero but not show highlights made in Acrobat — people would complain, rightly, that Zotero couldn't display standard PDF annotations.

If you just want to take notes — not annotations — about the document, you can create Zotero notes on the parent item, either from the library tab or by opening the Notes pane in the reader. Zotero notes aren't annotations and don't appear in the section you showed.

If you don't want to see the list of PDF annotations in the item pane, you can just collapse that section.

If for some reason you want to actually remove the annotations you created in another PDF reader, you can use File → Import Annotations from the reader, open the Annotations tab of the left sidebar, select all annotations, and delete them.

No, notes are just notes. They're child items of the parent item. There's a Notes button in the side navigation bar in the reader that will open up an editor on the right.

Annotations — of all the kinds I listed above, including highlights, underlines, and location-specific note annotations — are annotations on the PDF, and those are going to appear in the Annotations tab of the reader sidebar and the Annotations section of the item pane in the library view, no matter where they were created. Again, it would make absolutely no sense for a highlight that you create in Acrobat and a highlight you create in Zotero not to appear in the same list of annotations. Zotero has a built-in PDF reader. It supports many standard annotation types. You create them the same way as in other PDF tools. They happen to not be stored in the file while using Zotero, but that's a technical implementation detail — if you export the PDF, they'll all be embedded in the file as standard PDF annotations. I don't know why you have this idea that PDF annotations created in Zotero and PDF annotations created in another tool are somehow fundamentally different, but there's just no basis for that, and it's not what the vast majority of users would expect. This isn't going to change.

They're not "Adobe notes". They are PDF annotations, created and read by any PDF reader, including Zotero. It's a specific technical thing, and the fact you don't understand that and keep insisting that there's some difference means you kind of have trust us when we tell you that what you're suggesting would not make sense. Mendeley failing to support PDF annotations in a standards-compliant way is just an example of their app being shoddy, not something to emulate.

"no escape"? I'm not sure why you're making this so contentious? Our sole goal here is to help you. You've been using terms like "Adobe notes" that suggest a misunderstanding of the technical details, and I've been trying to clarify what's actually involved here, which has implications for how you should expect this to work.

You asked whether annotations created with Adobe would be displayed separately from annotations created with Zotero, and the answer is no and will remain no.

For your new questions:

1) can I create a note to page 5 with Zotero that is listed separately from highlightings in the right menu of Zotero? YES or NO

Currently, no. As I've said, the section is called Annotations, and it will show all annotations of any type. It may become possible to filter different types of annotations there in some way. That will definitely become possible in the Annotations tab of the reader's left sidebar, where there are already other filtering options (tag, color, etc.) at the bottom of the pane, and we'll be adding annotation type as a filter there. That wouldn't work as well in the item pane, which is already contextual based on what's selected in the items list, but we'll see what makes sense there. Annotations will be displayed directly in the items list in the next major version of Zotero, and it will likely become possible to filter the items list by annotation type in some way, which would accomplish the same thing.

Just to be clear, it is standard for PDF readers to display annotations in a sidebar without any sort of filtering options, and that's what Zotero does now. We go beyond that already in the reader sidebar, and we'll be adding other features to both the reader sidebar and item pane Annotations section, but you should understand that what you're asking for is not a standard thing. Mendeley not displaying the standard PDF annotations that are already in the file isn't a feature — that's just a limitation of the software. Mendeley has not historically demonstrated a lot of care for standards or interoperability.

2) can I create a note to page 5 that when I click on it (in the right menu of Zotero) will open the pdf directly at that page? YES or NO

Currently, no, but that's just because the display of annotations there was added recently. You can do this in the Annotations tab of the reader's left sidebar.

In a future version, it will be possible both to jump directly to the PDF page as well as to edit annotations directly in the item pane. In the Zotero beta, you can also already double-click on annotations in the items list to jump to the PDF page.