Your comments

The "Debug Log" setting logs client-side connections details including server answers and error codes. The log file is saved in Textastic under "Local Files" in the "logs" directory.

If you do indeed get a "login denied" error as this feedback topic suggests, then it means almost certainly that either the user name or password is wrong. The "login denied" error is displayed only if the server you are trying to connect to sends this error code.
I did use SSH tunnels in the past, so I do know what they are. I thought that you maybe just meant git over ssh, sorry for the misunderstanding.
I'm not sure what you mean. I can successfully clone repositories over SSH with Working Copy.

Did you contact Anders Borum, the author of Working Copy? Usually he is very responsive.
No, it's always binary.
Working Copy is indeed the best option at the moment. You can use the new "Open…" command in Textastic to open and edit files that are stored in Working Copy. You can then commit the changes in Working Copy. You can also use the recent files list in Textastic to open recently used external files.

I'm actively working with the developer of Working Copy to further improve the integration of both apps.

There are also bugs in iOS 8 that I reported to Apple that should be fixed soon to improve the behavior (namely Cocoa Error 256 when opening files using the document picker).
Textastic internally uses libcurl, which uses binary transfer by default.
For now, you can drag the file icon from Textastic's window title bar onto the Safari Dock icon to view it.