Looking for a translation plugin with specific features

Hello,

I need your help to find a plugin in order to have my site in multiple languages. I did some research but couldn’t find what I need.

The features that I want are.

1. Automatic translation of the pages using Google (or Bing)
2. Option to correct any wrong translations by myself (and every correction I made to apply in whole website)
3. Translation widget (or floating bar) that when a user select another language than the default, that switch stays on every page or post clicks after the selection, so doesn’t have to select the language that prefers every time changes the page.

Is there a plugin with that options ?

Thank you for the help