Any way to keep an html button pressed?

I would try CSS and use the border-style inset, personally.

<input type="button" value="Inset Border" style="border-style:inset;" />

For a list of different styles, please see this jsFiddle.

No, that's not possible.

I'd suggest you to use something like the jQuery UI Buttons. They support exactly this behaviour: http://jqueryui.com/demos/button/#checkbox