Google translate has an extension that translates text selection.
- It is free
- Auto detects the selected language language
- Offers the choice of destination language in the extension options
- Does not support keyboard shortcuts, but it can be configured to automatically pop-out either a window with the translation, or a clickable icon.
Edit:
You can find a Google Translate entry in the context menu as indicated in the comment by Steve. This enables the use of an AutoHotKey command to bind a hotkey to it. It would be something like
#t::Send {AppsKey}g