I have downloaded through Nuget the .net API of Eikon and started a proof of concept to display some fields taken from my Eikon and to display in a wpf app. It works well but I was wondering if I need to subscribe to something else to use it or is it part of my Eikon subscription?
If you intend to build a custom application running alongside Eikon, you don't need to subscribe to anything else. Eikon .NET SDK is included with your Eikon subscription.
If you intend to build an app residing within Eikon platform, then you need to join Eikon App Studio program. For more info see https://developers.thomsonreuters.com/app-studio
It may be worth noting that your contract with Thomson Reuters prohibits using Eikon and any APIs that come with it for data redistribution. If you intend to redistribute Thomson Reuters data, you need to contract for a product that includes data redistribution license.
Eikon .NET SDK is included with every Eikon account. No additional licensing is required. Any application built with Eikon .NET SDK requires Eikon at run time, i.e. it can only retrieve data from Eikon as long as Eikon application is running alongside. Data entitlements are enforced by Eikon. If user's Eikon account is permissioned to view a piece of data, your application will be able to retrieve it. If user is not permissioned to view a piece of data in Eikon, your application won't be able to access this data. As long as you don't redistribute the data your application retrieves (including things like feeding this data into a risk management or algorithmic trading system or some such), you're well within your contractual rights to develop an application with Eikon .NET SDK and use it with your personal or any other Eikon account belonging to your company.
Who asked you to obtain this "Data Application License"? And did they give you instructions how to obtain it? The term "Data Application License" is not something I've ever come across at Thomson Reuters. I don't believe we use this term at all. At least not in English.