1. How to use X?

X should work out of the box if you did not skip the X-Server installation in the initial setup. Simply open a connection and start a X application (e.g. "xeyes" like you can see on one of the screenshots).
If this doesn' work, you need to make sure that a) the X-Server is installed and b) the X-Server is running. Both can be controlled in the Preferences menu (Preferences->X-Server). To install the X-Server, click on "Download" to download the file "VcXsrv-portable-" and after that select this file by clicking on "Install". To start the X-Server, click on the "Start X-Server" button.

2. How to use the "Copy Files" feature?

If you right-click a connection you can open up a WinSCP session by clicking on "Copy Files". WinSSHTerm sends the connection configuration to WinSCP, so there is no need for manually creating a session in WinSCP and this is a good thing. Usually WinSCP will open up the user's home directory. You can change this by highlighting the full directory path in PuTTY before clicking on "Copy Files". WinSCP will then open up and automatically try to cd into that directory.
To enable this feature, you need to make sure that the portable executable of WinSCP is installed (Preferences->Copy Files). If you need to change some WinSCP settings (e.g. configuring a proxy), you can do this with command-line parameters. For more information please have a look here and here.

3. Which keyboard shortcuts can I use in WinSSHTerm?

Besides the shortcuts from PuTTY, WinSSHTerm provides additional shortcuts which are listed in the menu (Navigate->Shortcuts).

4. I need to change some PuTTY settings, but I can't find it in WinSSHTerm 

WinSSHTerm uses one shared PuTTY session (called "WinSSHTerm") for all connections. You can open PuTTY and manually change the session settings, which aren't configurable in WinSSHTerm and see if this works for you. However, if you manually change the session settings, then WinSSHTerm won't be fully portable any longer. All custom changes will be lost if you switch your computer or reset the PuTTY session file "WinSSHTerm". If you find yourself in this situation please contact me.

5. How to update WinSSHTerm?

If you're using the .msi installer edition, then simply download the new version and install it. To update the portable edition, download the new version, extract the zip and replace the file "WinSSHTerm.exe". In order to update the embedded tools like PuTTY or WinSCP, go to Preferences menu, download the new version and overwrite the old files by clicking on "Install".

6. Pressing the TAB key in the terminal client switches the tab

This bug was fixed in version 1.3.6. It is possible to switch the tabs with CTRL+TAB and CTRL+SHIFT+TAB - this is the standard keyboard shortcut for switching tabs in MS Windows.
Edit: This still seems to be an issue in very rare cases, which until now could not be reproduced. If you run into this problem, pressing the CTRL-key once should revert the normal behaviour.

7. The PuTTY terminal is UTF-8 encoded, but not WinSCP

WinSCP checks the environment variable $LANG on the remote system to decide whether to enable UTF-8 or not. If your $LANG is set to "POSIX", UTF-8 will not be enabled. To enable UTF-8 in WinSCP, set the $LANG to e.g. "en_US.UTF-8" or add the command-line parameters "/rawsettings Utf=1" in Preferences->Copy Files.

8. I've lost the master password

Without the master password it's not possible to decrypt the stored passwords, including the password for the shared connection file and its template variables. If you have lost your master password, then manually delete the file "key" in the "config" folder and start WinSSHTerm. It will start without the password prompt, but all encrypted data will be deleted.

9. Setting custom terminal colors (workaround)

Currently WinSSHTerm supports only the color schemes "WinSSHTerm" and "PuTTY". However, it is possible to use a custom color scheme by following these steps in the exact order:

1.) Start WinSSHTerm and go to File->Preferences->Terminal
2.) Choose Color Scheme -> ignore and click on Ok
3.) Import the custom color scheme reg file into the PuTTY session "WinSSHTerm" (you can also manually edit the colors with PuTTY)
4.) Open up a new connection and you should see the new color scheme

Please note, that this is only a workaround (more info in section 4.).

10. Sorting the connections tree (workaround)

Sorting the connections tree automatically is currently not supported. However, as the connections are stored in a XML file, you could sort the connections by using an external program like XML Sorter. In XML Sorter, just open your "connections.xml" as source (be sure to make a backup of this file and close WinSSHTerm before). If you want to sort all connections by name, then select Options->Sort by specific attributes->Name and click on "Sort". Now wait until the sort process finishes. You should see the sorted XML in the "After" textbox. To persist the changes select Target->Overwrite source file and click on "Save".