I can tell you what worked for me, what i did was this created a new bookmark folder in Safari on your iPhone is a breeze. Here's how to do it:-
1. Open the Safari app.
2. Tap the Bookmarks icon. It looks like an open book.
3. Tap Edit in the bottom right corner.
4. Now, tap New Folder at the bottom left corner.
5. Give your new folder a descriptive name.
6. (Optional) Choose where you want to create this folder. By default, it goes to "Bookmarks," but you can select a different existing folder if you prefer.
7. Tap Done to save your new bookmark folder.
Follow for more details assistance below.
https://www.youtube.com/watch?v=BDJ-W08it44&ab_channel=TheGeekPage

Hello again, Francesco.  Thank you for the progress report.

fqm78 wrote on Mar 18^th, 2014 at 4:21pm:
Hello again, Francesco.  I understand that you have thought deeply about how syncing must work.  However, we have thought deeply about it also

Delete unmatched items will not delete new items.  Here are the reasons why:

• During Imports, Delete unmatched items runs only once, after all Clients have been imported, and only bookmarks which have not been matched in ANY client are deleted.  Therefore, new bookmarks will not be deleted.  Also, when you add a bookmark in, say, Safari, only Safari is imported.  Chrome is not imported.

• During exports, Delete unmatched items will only delete items which are not presently existing in the BookMacster document.  This is what you want.

Therefore, by default BookMacster switches all Delete unmatched items ON (flagged), because this gives the syncing that most users want.

fqm78 wrote on Mar 18^th, 2014 at 4:21pm:
If you leave Delete unmatched items switched OFF, then you will get doubled folders and stuff like that.  If you switch the  Delete unmatched items checkboxes back ON, then the changes you make in Safari or Chrome will be imported by BookMacster.  However, we do not recommend doing significant reorderings and rearrangements, which we call "housecleaning", in browsers while BookMacster is syncing.  The reasons are…

• BookMacster will periodically interrupt your work when it syncs bookmarks.  This will be annoying to you.

• If you make changes while BookMacster is syncing, BookMacster will need to sync again.  This will be more annoying to you.

• If the numbers of changes you make between syncs exceeds the Safe Sync Limits, BookMacster will ask you to confirm whether you want to make so many changes.  This will be annoying too.

• With all the syncing and annoyances, some intended bookmarks changes may be overwritten.

For these reason, we recommend the following procedure for doing significant housecleaning in a synced BookMacster document:

• Open your document in BookMacster.

• Click the Syncing button in the toolbar, to Pause syncing.

• Do your reorderings and arrangements in BookMacster.

• Click the Syncing button in the toolbar, to Resume syncing.  BookMacster will prompt you to Export.

• Click the Export button.

• Close the document and quit BookMacster.

fqm78 wrote on Mar 18^th, 2014 at 4:21pm:
Indeed syncing is tricky and there are many other little tweaks in the algorithm which we have finely tuned over a period of years, to give the syncing results that users expect.

Ok Jerry,
I followed your instructions (the screencast was very simple and well done!), it seems all has gone where it should be...
Creating a new file was the simplest, fastest and most effective solution, thanks a lot!! 
Now I'm going to set up a reliable workflow to make bookmarks land from chrome or safari and synchronize.
I'll let you know if get problems.
Thank you,
bye,
Francesco

Hello, Francesco.

BookMacster should sync the Favorites Bar in Safari to the Bookmarks Bar in Chrome, and in BookMacster itself, with no special special setup.  Mapping as you want is the default mapping in a new Bookmarkshelf document.

Regarding the BookmarksBar folders that you see in Chrome, with no space between Bookmarks and Bar, I would advise that neither of these are the real Bookmarks Bar in Chrome.  They are phony.  They are just ordinary folders which were probably created by some application, importer or exporter that did not know how to handle the Bookmarks Bar.  To reduce confusion, I recommend that you move all items in those folders into different folders, into the real Bookmarks Bar if that is where you want them, and then delete the empty BookmarksBar folders.  You can do this either in Chrome or in BookMacster.

I don't know where your bookmarks are right now.  If your bookmarks are all in Safari and Chrome, you may wish to trash whatever Bookmarkshelf document file(s) you have in Safari by activating it and clicking in the menu: File > Close and Delete.  This will get rid of any non-default mapping settings.  Then please watch this short screencast I've just created, which shows how creating a new document will automatically merge together the Chrome and Safari bars without tweaking any settings.  Near the middle of the screencast, when I click Sort All is where you might want to move items out of the phony BookmarksBar folders and delete them.

Let us know if you have any more questions on how to get from wherever you are.