First issue. I'm assuming you've installed the program? The "icon" you see is the installer program. If you don't need it then yes, it is safe to delete. However, for now, if I was you I'd just move it to my Downloads folder (C:\Users\ your user name\Downloads).
Second issue. If you want a desktop icon for a program where the option wasn't available. Locate the programs folder, either in Program Files or Program Files (x86), and look for the .exe file in there. Right click it, mouse over SendTo and select Desktop (create shortcut).
Hope that helps.