For 1: you can try and access the af:query component and call getChildren() to see if you can get a hold of inner components (e.g. buttons). By default, the access key for the advanced mode button is not exposed.
For 2) Same as for 1. This is not exposed and all you can do is to check if getChildren issued on the RichPanelCollection component reference allows you to access the command button and then set the access key to it
Meanwhile I'll file an ER to make access keys generally accessible for change (which however may take time before this gets implemented)
Access keys are browser and OS dependent. Some browser uses Alt+Key combination and some uses Alt+Shift+Key combination. Refer the documentation for more details : Oracle ADF Faces - <af:goButton>
Check out the accessKey property.
Have you also tried overriding the resource bundle key by adding & in front of the key you want to use as access key? Check out the resource bundle key (Expand Resource Styles) used by them in the ADF Component Demo :query Skinning Key Demo
I tried af query component's getChildren() which returned a Panel Group Layout.
Yes this is expected. To get a a hold onto specific components in a complex component like af:query deep iterations may be required. So call getChildren on the panel group layout and so on until you find the button to change