Deleting System Options from the Start menu

You can actually remove the Find and Run options from the start menu by performing a simple registry hack. Again like always Launch the registry editor and scroll down to the below key: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer Right-click on the right pane and select New, DWORD Value. Name it NoFind.(To remove the RUN option name it NoRun). Double-click the newly create DWORD to edit it's value and enter 1 as its value. This will disable the FIND option of the Start Menu and will also disable the default Shortcut key(F3 for Find.) To restore the Run or find command modify the value of the DWORD to 0 or simply Delete the DWORD value.

How to remove the shortcut arrow from the desktop ?

Open Regedit and navigate to the following key:
HKEY_LOCAL_MACHINE \ SOFTWARE \ Microsoft \ Windows \ CurrentVersion \ Explorer \ Shell Icons Backup the key. More information.
In the right-pane, create a new String value named "29"
Double-click 29 and set its data to:
C:\Windows\System32\shell32.dll,50 (an empty icon)
Close Registry Editor.
Now,
Right-click Desktop, choose Properties
Click the Appearance Tab.
Click Advanced button.
Choose Icon from the drop-down list
Set it's size to 31 and press OK, OK.
The changes will be applied now. Repeat the above steps and then set the Icon size back to 32 (defaults). The above steps are required to force Windows to redraw the icons