I am unable locate any information on the Internet that simply makes the statement, "Office Add-ins (aka Apps for Office) only work in Desktop apps and Office Online. They do not work in SharePoint office web-parts.", if that truly is a correct statement.

I have a Excel Add-in and can published it using the following instructions: https://msdn.microsoft.com/en-us/library/office/fp123515.aspx . My add-in is a task-pane add-in (https://msdn.microsoft.com/en-us/library/office/fp123523.aspx)

With Desktop Excel 2013

A1. I can publish the app's manifest to an app-catalog that's on a file share, then set up trust to that share on the desktop version of Excel. Then desktop versions of Excel is able to insert my Add-in into a spreasheet.

A2. I can publish the app's manifest to an app-catalog on SharePoint, then set up trust to the SharePoint's app catalog in the desktop version of Excel. Then the desktop Excel is able to insert my Add-in into a spreadsheet.

With Excel in a web-browser

Using Office 365:

B1. I can can publish my app's manifest to a Office 365 site's app-catalog. Now when I open a spreadsheet stored in a Office 365 site document library, it launches "Excel Online" from which I can insert my app into the spreadsheet. Note that: when viewing the spreadsheet by clicking on it from the document library, the url shows that WopiFrame is used.)

Note in the screenshot below, in the Insert tab is "Office Add-ins" button.

B2. When I embed that same spreadsheet into a site Page, using Excel Web Part, and enabled the web-part setting "Display Task Pane Apps" (which is off by default), I don't see the task-pane. Why not? (question 1)

Using on-premise SharePoint 2013

Using the SharePoint 2013 admin-panel, I create an app-catalog for the entire SharePoint application (there's only one). Then under the "Apps for Office" section, I upload the manifest to my site. Now I go to a document library containing an Excel spreadsheet and launch the web viewer the request to edit the Spreadsheet in the web site. However, there's no "Office Add-ins" button. See screenshot:

Is it possible to host an Excel Office Add-in task-pane part inside of SharePoint 2013? (question 2)

I tried configuring for both Excel Services (xlviewer.aspx) and Excel Web App (WopiFrame2.aspx)

The Future

This SharePoint 2013 is installed and configured with an Office Web Apps installation. I understand that SharePoint 2016 will require "Office Online Server", the successor to Office Web Apps. This seems to infer that if the functionality I'm talking about is not available in SharePoint 2013 that will be available in SharePoint 2016. Is this the case? (question 3)