I read that you could use Bluetooth Keyboards since a certain Windows Phone 8.1 version. What update do I need for this and how do I connect the keyboard to my phone? And does this work in every app?
Bluetooth keyboards are only supported with Windows Phone 8.1 Update 2 which will only be released officially on a select set of phones (ie. not all WP8 phones).
Currently, the Lumia 640 and 640 XL come with Update 2.
For most other phones, it is possible to install Update 2 unofficially as part of the Windows 10 for phone preview programme. Phones install Update 2 as part of the process before Windows 10 is installed.