Below is an image of a very simple Custom Gadget.  

The quick answer to the question "What Traditional Context Information is Passed to a Custom Gadget by the Interactive Dashboard?" is nothing!

Although the HTML of a Custom Gadget can be produced using an ASP or ASP.NET page, there is no contextual information actually passed to the Custom Gadget in the URL of the Gadget (document.URL).  This is because the URL of the Custom Gadget sits within an iframe so that all contextual information resides in the parental frame of the Custom Gadget.  The URL that calls the Custom Gadget is very simple e.g.

http://[servername]/[installname]/custompages/Gadgets/simpletwittergadget.html

or

http://[servername]/Gadgets/simpletwittergadget.html

Another article will discuss the creating the code for the Custom Gadget.

BUT

In the example above the Interactive Dashboard redirects to the Custom Gadget with a path that is actually accessible in the Client Side document.referrer property, this would look something like this

http://localhost/crm//InteractiveDashboard/InteractiveDashboard.asp?SID=164017957441086&contextEntityId=-1&contextRecordId=-1&contextDashboardAction=1180&contextKeys=Key0:4_Key4:1 

The document.referrer contains the SID or Session ID which means that this can be used for either SOAP or REST based web service requests.  Sage CRM v7.1 allows the SID to be appended to the URL of SData requests as an alternative authentication mechanism.  This allows SData to be used in AJAX calls within either Custom Gadgets of in other parts of the main interface.

For a further discussion about contextual information available to Classic Content Blocks within Interactive Dashboards please see the article "Using Classic Content Blocks in the Interactive Dashboard".

For more information about using SData in AJAX requests in Sage CRM v7.1 and onwards, please see the article "Grabbing Serverside Information using a SData Webservice call (AJAX)".

For more information about using SOAP Web Services in all versions of Sage CRM, please see the article "Grabbing Serverside Information using a SOAP Webservice call (AJAX)".