Is it possible to create an icon on home screen to a specific note?
Unfortunately there's no url scheme for the Notes app, so there's no way to jump to a specific one. 

There are two good sites for finding iOS app url schemes, handleOpenURL and the iPhone URL Schemes page on Akosma's wiki. The former has many more urls, but the latter occasionally has something the other doesn't.

A quick search in handleOpenURL for "text" and for "note" only shows one app that appears that it can do what you want (which doesn't mean it's the only app that does so, just that it's the only one listed in the site), though even then I'm not certain you'll be able to create the shortcut by hand. 

I'm completely unfamiliar with the app and have no idea whether it's worthwhile, but I figure it's worth passing on: Notebooks for iPhone.