Question: After swapping my language and input options about (UK layout and German layout) to support the two keyboards I have, a certain key will stop working partially depending on the layout.

If I swap my input method to UK, the apostrophe/at-sign key will stop working. Windows 10 will make a tone sound when pressed twice, and if held it will input many of that key, as should be the case.

If I swap the the DE layout, the would-be apostrophe key works fine, but the colon/semicolon key (Ö on the German keyboard) stops working unless held.

I'm certain it's not a hardware issue, it must be to do with Windows 10.  

What's going on and how do I fix it?

Answer: 
I solved this by removing a mistakenly added 'change layout' shortcut, to the grave (`) key, oddly affecting the apostrophe and ö keys on the other layouts.

To fix this:

* Context-menu/Right-mouse on the Language Bar on the Windows taskbar
-> Settings/Einstellungen
* In the third section, "Change the Input Method"/"Wechseln der ingabemethode", open the blue link at the bottom, "Change the shortcut keys for the Language Bar"/"Abkürzungstasten der Sprachenleiste ändern"
* From there,
remove the setting for "Change Input Language"/"Zwischen
Eingabesprachen" from whatever it is (mine was Graviszeichen (`)) to
None.
This exact thing happened to me and this thread lead me to the answer. 

The language bar, for whatever reason, wasn't present on my taskbar so I went into Windows 10 Settings/Time & Language/Region & language/Advanced Keyboard Settings/Language Bar Options.
In there I went to the Advanced Key Setting tab and selected "Change Key Sequence...". In the box that appeared I set both options to "Not Assigned" and the issue was resolved.