There is certainly influence in many directions. For example, some of the GWT and Dart compiler folks were inspired to do better by a presentation at Google about TypeScript, and ideas from AtScript were picked up by TypeScript.
"Just stop what you're doing" isn't helpful. People need to write code today, and we have solutions for them.
Less than you'd think. Starting from scratch is easy at first since you have no users and freedom to do what you like. Maintaining a popular project well requires more creativity in some ways because design constraints built up over time.
Improving the web, in particular, requires that people think like maintainers and innovators.
"Just stop what you're doing" isn't helpful. People need to write code today, and we have solutions for them.