In regard to your request to have a Yahoo Mail icon in the IE "Taskbar" I'm not sure which toolbar you’re referring to in IE, because IE has the following toolbars:
Menu Bar, Favorites Bar, Command Bar, and Status Bar.
If you’re referring to the Command Bar, although you can’t directly put a Yahoo Mail icon there, as a work-around, you can add a “Home” link, and add your Yahoo homepage or Yahoo Mail (or both) to that. (I've done that for both Yahoo Mail and My Yahoo, and they are extremely easy to access.)
First, customize the Command Bar:
Open IE, click on View, Toolbars, and check the Command toolbar. Then, to customize the Command toolbar, put your cursor on the toolbar, right-click, and then at the bottom of the list, select Customize. There you can choose your options, including Add or Remove Commands. Add the Home icon.
Then, go to the website that you wish to add to your Home Page settings.
From that website, open IE, in the Command Bar go to the Home link and click the little down-arrow 6 to the right of the Home link.
Select Add or Change Home Page
A menu will open that says: Would you like to use the following as your home page?
If you wish to add this webpage to a list of “Home pages” then click: Add this webpage to your Homepage tabs.
If you wish this webpage to be your only Home page, then click: Use this webpage as your only homepage.