Moving a folder in SVN

Your problem is having used the wrong command; 'Switch' does the exact complement of what you wanted - it changes the repository location your working copy 'points at', without changing the repository. (Switch then commit would have produced some result, but in a really broken way which isn't what you meant. You were right; the tempting-sounding 'Relocate' is a special case of 'Switch', and should be avoided for the same reason.)
The 'Update' command then updated the working copy to match what was currently in the repository at the 'new' location - nothing!

Subversion doesn't have a true move/rename yet. The subversion-safe way to do it is to copy and then delete. TortoiseSVN includes a handy 'move' option which does a copy-and-delete as one operation.

The easiest way to do what you wanted:
1. Open repo-browser in TortoiseSVN.
2. Right-click and drag the folder from its old location to the new one.
3. Select 'Move' from the context menu.

This also works inside your working copy, and is the safe Tortoise/Subversion way to move or rename files and folders in the wc without losing history.

to answer your second point, here's how I move folders with Tortoise-SVN:

• right click in Windows explorer on a folder, then 'Tortoise SVN', then 'Repo-browser'.
• in repo browser, make your you are looking at where-the-folder-you-want-to-move-is.
• click on the folder (or file!) to move and drag it on the left pane where you want it to be
• click OK to close the repo browser
• right-click in your folder and 'Update'.

When you update, Tortoise SVN will delete the folder where it was and re-create it where you moved it.

To move the files properly, use the move command.

EDIT:
Note, move, mv, rename, ren are aliases for the same command. It can be found in TortoiseSVN under "TortoiseSVN" -> "Rename..." see here