Check what shortcut is used for Emoji & Symbols by clicking the Edit menu in most apps. Here is mine showing fn-E:
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Also what do you have at: > System Settings > Keyboard > Keyboard Shortcuts > App Shortcuts. Open the disclosure triangle next to All Applications:
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You can override the Emoji & Symbols shortcut by clicking the + button. Enter the name "Emoji & Symbols", then a different shortcut.
Use the same procedure for dictation using the name "Start Dictation..."
Another setting to check at > System Settings > Keyboard. Change the setting "Press fn key to" to "Do Nothing". Your setting may say Globe key depending on your keyboard.
Is it possible that your Function/Globe key is stuck? This would allow typing to continue like normal until the "e" is pressed.