No problem. AndFTPPro acts as unlock key only. There is no icon for it.

Are you able to preserve timestamp with any FTP client?

You want to preserve timestamp on upload? Are you using FTP or SFTP or SCP?

You can add it to home screen by long press on it, then drag and drop on home screen.

EHOSTUNREACH (No route to host) error is quite clear. Android device cannot solve route to the server. It's a network issue, it could come from firewall or router.

What do you have for "Wake lock" option? Enabled (partial) or Enabled (full)?

Some users report that they get empty list when connecting to some SCP server. 99% of such issue come from date format. There is no standard date for SCP so the list entry parser consider the line as corrupted. Here after a sample for Russian date: drwxr-xr-x 3 test test 4096 нояб. 1 19:58 . drw...

You need to enter either hostname of your PC/Desktop or server. You can also enter IP address. Both are supported. I recommend IP address if you get in trouble with hostname.

Could you provide a testing account so I could try to reproduce the problem from here?

It should work but we've not tested it (that's why it's not documented yet).
The key is "ftp_overwrite" and possible values are "overwrite", "skip", "prompt".

Try it and let me know if it works as you need.