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Hmm, weird.
What happens when you go to System Preferences -> General and uncheck the checkbox called "Close windows when quitting an app"?

That sounds like the Working Copy file provider extension crashes.
Please try to reboot your iPad. If that doesn't help, please contact Anders Borum, the author of Working Copy and ask him for advice.
Yes, I've seen that. That's excellent news.
You can add custom syntax definitions to Textastic by using TextMate bundles. See
http://www.textasticapp.com/v6/manual/lessons/How_can_I_add_my_own_syntax_definitions__themes_and_templates.html
A quick search for "taskpaper tmbundle" in Google brought up this TextMate bundle which should work:
No, currently this is not supported, sorry. Previously this wasn't allowed by Apple at all, but they recently made some changes to the App Store guidelines which I'll look into.
You can add custom syntax definitions to Textastic by using TextMate bundles. See
http://www.textasticapp.com/v6/manual/lessons/How_can_I_add_my_own_syntax_definitions__themes_and_templates.html
A quick search for "Kotlin tmbundle" in Google brought up this TextMate bundle which should work:
Ok, I just saw that on macOS, the code completion window is not visible if the window is maximized and you are editing in the last line. That's definitely a bug. I've added it to my todo list.
Currently it is not possible, but I'll consider adding some extra space after the last line so you can scroll down further.
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You can also try to delete the folder that contains the saved application state: