Your comments

Yes, these are all things that are on my todo list :)
Just create a folder before you download and then download the files into that folder by selecting it on the left in the File Transfer screen. 

There's no need to download it to the root folder first and moving it afterwards unless I'm missing something.

Moving files is implemented similar to how you can move mails in Apple's Mail app.
Textastic uses the Discount Markdown library: http://www.pell.portland.or.us/~orc/Code/discount/

It supports Markdown and some extensions: I have compiled it with "--with-fenced-code" and "--enable-alpha-list".

Have a look at the Discount site to see what it supports.
Yes, you can tap on the action button and choose "Copy Generated HTML" to copy the HTML generated by the Discount Markdown library.

You can also directly send it as an HTML-formatted email by choosing "Send As Message" in Textastic.
Then you have to delete the app and reinstall it. 

Note: All your data and settings in Textastic are lost when you do that.
Apple's Mail app shows a light blue background for the current mail but doesn't select it when you tap on the "Edit" button. I think this would be a good solution. I'll consider adding this.
Hello,

before you tap on the "Edit" button in the Files section, the current file should be marked blue. This allows you to see which one is the current file, doesn't it?