Howto write modules to storage?

I think you've misunderstood - there is an actual button for uploads!

• Go to https://www.espruino.com/ide/
  
• Connect to your device
  
• Click the Storage icon (4 discs, basically in the middle of the screen)
  
• Click Upload Files
  
• Upload your file using the file chooser
  
  

Uploading your way will work but as you noted it's messy!

In your case, you can ignore the "exports" is not defined error. It's because after upload the IDE is trying to run your module as if it's a normal app - but it's a module.