After some effort
[forum.textpattern.io], Textpattern (clear, smart, and the highest quality CMS, IMHO) developers have promised
[forum.textpattern.io] to publish support for Hiawatha, if such instruction will be documented — how to run Textpattern CMS on Hiawatha webserver. My English is weak, although not so much to document, perhaps URL Toolkit is sufficient? And, of cause, not to forget to enable UseFastCGI, StartFile = index.php, too.