Q: How can I add mail icon to menu bar?

If Mail is not running, launch it by selecting Mail from the Mac's Applications folder. Then, drag the Mail icon from the Dock to some other location in the Dock. It will stay there, even after you quit Mail.

I'm not aware of a way of doing that without modifying OS X, which I do not recommend. Instead, I suggest investigating alternate ways of switching among running applications, some of which are described in the following Apple Support documents:

Mac OS X: Additional features of the Dock - Apple Support

You might find the Application Switcher to be useful.

Also,

Mac Basics: Launchpad is the fast way to find and open your apps - Apple Support

and

Mac Basics: Notifications keep you informed - Apple Support

Switch Basics: On Windows, I used to... - Apple Support

You might find this useful too: http://www.apple.com/support/macbasics/

Sure. There is at least one non-Apple program that does what you describe, but it modifies OS X and as such I am not willing to recommend it. If you want to do that anyway, search for a program called "Mail Unread Menu", but beware that software not obtained from the Mac App Store involves a degree of risk due that only you can decide to accept.

Don't install anything without knowing in advance how to uninstall it. To learn how to use Time Machine read Mac Basics: Time Machine backs up your Mac - Apple Support.

• Never obtain or install any program from a source other than one specifically authorized by the program's developer. This precaution has become more important as Apple's popularity has grown in recent years. It's a trivial matter for anyone to effectively hijack a program distributed through the Internet, surreptitiously incorporate malicious software, and subsequently host it on sites not authorized by that program's developer. Those sites generally appear more prominently in a web search than legitimate ones because they also include revenue-producing advertisements that benefit the search engine you choose to use.

The Mail icon in the Dock already does exactly what you describe, but it's in the Dock. It is built in. Seems like a minor distinction to me, but I realize everyone's needs are different. If you think it can be improved upon tell Apple: http://www.apple.com/feedback/macosx.html.

If it's a Mail replacement you're seeking, there are many alternatives. I don't use any of them personally.

You're welcome!

http://www.macupdate.com/app/mac/22042/mail-unread-menu worked for me on Mail 9,2 app it shows the unread mails in the Menu and not the dock which I always have hidden hope it works