Not really possible using script, not with any consistent results on the client side.
For example, the behaviour you've mentioned regarding the window opening as a tab on the browser - that's a user specific browser setting. There's no way you can override this, so how your page will display will vary from user to user - not something you want
As mentioned, you could create a Winforms \ WPF app that hosts a
browser control[
^] inside the application. When this application launches, to could set the browser control to load your web page and display as a 'web app'.
You would have full control over this and could style it however you wanted.
After reading a couple of your other comments - just design a decent website, that's the only way you'll be truly cross-platform compatible. Forget about removing tabs, menus etc. They're part of the browser and all browsers behave differently and are customisable by the user. There's no 'one bit of javascript' that could do what you want on all os's and browsers, security wise - can you imagine the carnage that would be happening if random websites could just take over your browser and start doing things like this?!!