Problem with the long menu text.

Your flashes menu needs to be bigger in height to fit that sub menu. Also background images are just not wide enough to cover whole surface of menu you need images with bit bigger width.

Items font size is 9px so making them smaller is I suppose out of question.

For other question did you use menu item alias type for menu item when you created second menu item that points to same article?

I must set the root menù to an single article, because i had not thought to mobile devices?
you have to touch the main menu(with postback)to bring up the second level menu and of course the third level is unattainable with touch devices.
I don't think you can solve these problems!

Open templates\hot_flashes\flashes_menu\menu.js

for devices:

line ~82

jQuery('#flashes > li > a').mouseover

change to:

jQuery('#flashes > li > a').click