Is there a central collection of information about the often called right brain phenomena? There are mental states that some have termed right brain e.g. "Drawing on the right side of the brain" but which may be incorrectly described.

Is there a site that specializes in information on mental states called "right side"?
The chapter on Hemispheric Specialization from Cognitive Neuroscience (Gazzaniga) is a good place to start, and I am reviewing some of it here:

In general, right side / left side  thinking has been abandoned for a systems view of cognition where both sides contribute to a given task but maintain certain specializations due to how the brain interacts with the environment as it develops, ( we still don't have all the facts though).

For instance, 96% of humans have a left-hemisphere specialization for language and speech ( processing spoken input into words and linking to meaning), yet the right hemisphere is linked to prosody as well and both report to frontal areas (where  higher associational meaning and/or task specific operations are performed so here again it could be left or right), so when hearing a conversation you are most likely using both an projecting to one or both sides of other parts of the brain depending on context,task, motivation etc, and shifting operations dynamically.

The inverse can also happen, the right hemisphere is traditionally attached to artistic thinking, yet this claim falls flat on it's face when you consider visual processing is equally divided in between hemispheres at it's early stages, the confusion stems from higher visual processing, where some visuospatial processes end up in the right side (location), but still some other processes like visual discrimination end up on the left side.

The problem with making a map of left and right areas of specialization, is that due to plasticity and the unique upbringing of each person,plus perhaps genetic variations, these areas don't overlap from person to person, so a capabilities map of general areas makes more sense for now.