Magento 2 – How to Add Custom CSS Files into the Head

Bottom line: you need to have a value calculated by PHP, therefore the approach of using a helper is appropriate. I think it makes sense to use the addCss convenience method rather than addItem a it's a little cleaner and should work fine for your needs:

<{handle}>
    <action block="head" method="addCss">
        <stylesheet helper="my_module/my_helper/getFileName" />
    </action>
</{handle}>

Your helper seems to be calculating the path to the CSS files using the design model, but this will be done again by the page/html_head block. Change your helper to simply return the file paths relative to the theme (i.e. not using the design model) and your problem is solved.

Use the STORE layout handle:

<?xml version="1.0"?>
<layout version="0.1.0">
    <STORE_en>
        <reference name="content">
            ...
        </reference>
    </STORE_en>
</layout>

Where en is the code of the store in question. This will add the layout changes to all pages for that store in the same way as the <default> layout handle does for all pages of all stores. By default there is no way to use the STORE layout handle and only have layout changes for certain pages in that store.

FYI, next time just create a new question rather than completely changing an existing one so the comments don't make any sense - SE is a resource for people to refer to in the future as well as a way for you to have your questions answered.