Your comments

Actually, the status bar can be disabled (games do that usually) and I would probably hide the status bar and the toolbar if I implemented such a mode.
I see – I could add a setting for this.
Which highlight do you mean, exactly? The blue vertical cursor that signals the current position in the text? Or the highlighting of the current line?
Did you try to restart the app or the iPad and see if this helps (as described in my other comment)?

Does it happen with a particular file?
This options already exists: just open the File Properties popover and choose the first entry "Plain Text" as the syntax definition for this file.

This disables syntax highlighting.
That shouldn't happen – maybe it's just a glitch. Did you try to restart the app and see if it works then?

(You have to press the home button to suspend the app, double-press the home button to bring up the list of recently used apps, hold your finger on the Textastic icon and tap on the red "minus" sign to quit the app – or just do a full restart of the iPad)

If that doesn't help: can you maybe post a video so I can try to reproduce the problem?
The menu appears when you either (slowly) tap two times at the same location or when you do a (quick) double tap somewhere in the text.

It also appears when you tap and hold to bring up the loupe and then release the finger from the screen.

This is more or less the standard behaviour on iOS.
Thanks for mailing the example file. I could reproduce the problem and will try to solve it for the next update.
I just tried this on my server and it works.

This might be a problem with a specific type of FTP server.

Which FTP server (product name, version number, running on which OS) are you connecting to? I appreciate any information that allows me to reproduce the problem. A demo account would be excellent.