I am trying to create chrome extension that will create floating overlay (static one that dose not refresh), Similar to firefox add-on "ui sidebar"
Is there any way to maintain iframe like overlay that wont be effected by the page, and wont be reloaded when the tab reloads.
The simple answer is NO.
What you are describing is basically called browser chrome, i. e. UI. The only chrome Google Chrome extensions support since forever are page actions and browser actions.
Opera also supports sidebar actions. Rumor is, Firefox WebExtensions will support that too.
Chrome has no support however. It's on the wishlist but has no actual proposal/intent to ship. Apparently, there has been a recent decision not to pursue this.