Find Permission and perform action based on Admin access

Find Permission
SPWeb thisweb = SPControl.GetContextWeb(Context);
isAdmin = thisweb.DoesUserHavePermissions(SPBasePermissions.ManageLists);
if (isAdmin == true)
{
// todo
}

Permission for SPSecurityTrimmedControl

you can use SPSecurityTrimmedControl to customize as per the security.

'<' SharePoint:SPSecurityTrimmedControl PermissionsString="AddAndCustomizePages, ManageLists" runat="server"'>'

'<'/SharePoint:SPSecurityTrimmedControl'>'

The content within the control will be shown based on users access level.

The permission are like..
AddListItems
EditListItems
DeleteListItems
ViewListItems
ApproveItems
OpenItems
Zac Smith has listed all of them here

Failed to verify user permissions" error when using DspSts.asmx web service

have u enabled anonymous access at web application level?

more here