I recognize that the web leads to its own problems because it is platform independent, but if most of your visitors are Windows users than using Windows standards might make sense. Here is one site from Microsoft on UI design: https://msdn.microsoft.com/en-us/library/windows/desktop/ff728831%28v=vs.85%29.aspxpage from Microsoft on UI design.
User testing would really be the best option in this scenario. This may be common knowledge to everyone here but I'd recommend the work of Jakob Nielsen who has been writing about web usability for over 20 years and created a collection of web usability articles.
From personal experience working with people with very little training in how to use a computer, the X in the top corner is very commonly understood and should not be removed. Also be clear if there is a need to differentiate between "close" and "cancel".