EDIT Sorry I missed the browser part, so this answer may be irrelevant.
You should probably use some engine which already includes a lot of logic that many games use. You'll spend many months building it yourself, otherwise. Unity seems to be a popular one.
I believe that for professional game development, C++ is the dominant language. But others are also used, especially for smaller projects.
Open source is nice because people might help you. That is very unlikely until you have some working version though - there are a lot more aspiring game designers in need of help than there are programmers with too much time. Another advantage of open source is that others can reuse parts of your code (which is clearly an advantage for them more than for you).