I'm converting the legacy safari extension to safari app extension too and have some answers for your questions:
- Because app extension is more as functional extension then safari browser extension and could bring more features to you. And as per Apple says: safari app extension gives more communication and data exchange between Safari and your native app, docs.
But I have no more ideas if you only want an extension for safari why this is only way to do extensions.
- Yes, you should use the Cocoa App template. If you don't need the window for your app, you can remove it simply in Main.storyboard or make app as a "service".
- A lot of docs from Apple I've read but understood a bit then expected. So I found some youtube channels (they are 2 or more years old but some things seems don't changed) Some vieos here and the Osx Dev Daily playlist on this channel. And of course official swift docs if you select swift for your app as PL.
- I haven't read about this, but think it must be submitted with your Cocoa App.
- First of all you should to run your app target and only after this you should run your extension target and choose "Safari" in showed window to run in. If you have no the signing at the moment so ensure to enable "Allow unsigned extensions" in
Development > Allow unsigned extensions
in Safari app.
- Don't meet this info, could you share it, pls? (sry, don't have enough knowledges)
Hope, it helps to you!
P.S. also recomend to see the converting docs, but it may be insufficient for converting :)
EDIT: it's seems to be incorrect to remove app window or change the default menus created by Cocoa App template for app submit for App Store. Some people got negative decision of app submit because of menus changes of redundant items or app have poor functionality or has not it at all. So consider to read the submit docs.
Please, share your experience when you'll have success app submit!
EDIT 2: Today I found template in Xcode 10.1 that can be used for Safari Extensions directly. It is as previous workflow (template Cocoa App + add extension target) but there is safari extension target already included
The app window and menu is simplified for developers:

So you don't need work with your app and you can concentrate on extension only.