I installed linux mint on an HPG60 Notebook Lap top along side Windows 7. I have completed updates and have successfully downloaded and used various programs.

My pointer burys off the left side of screen.

I placed a few shortcuts on the desk top , they don't show. I did see my "Home" short cut for a few minutes but when I restarted it was gone. Upon placing other short cuts, they just do not appear.

My Lap Top display doesn't work, I need to use a flashlight to see it. I am hooked up to an AOC 22" L22H998 Envision Peripherals, (Which is detected and recognized by Linux Mint via HDMI.This display works fine on this same laptop and on others using Windows 7, 8 and 10.

What can I do to see my short cuts and to stop the pointer from burying off the left side of the desktop?

Linux Mint 17.2 Cinnamon 64-bit
Cinnamon Version 2.6.13
Linux Kernel 3.16.0-38-Generic
Processor Intel 2 Duo
CPU T6600 @ 2.20GHzx2
Memory 3.8GiB
Hard Drive 95.3GB
Graphics Card Intel Mobile 4 Series Chipset Integrated Graphics Controller

I haven't been able to get any search results for this. My desktop seems larger than my display. Does anyone have suggestions as to search terms I can use? I definitely want to get this figured out before I install Linux on my Newer system. I though I should add that the same thing happens on the Laptop display. Even though the display light is out, I can see it when shining a flashlight at a low angle upon the screen.

That's probably just the external screen not having the correct resolution.

Click on "Menu" (bottom left of desktop) - type in "display" (no quotes) and hit "Enter". Try to set the external monitor to its native resolution - guess if you have to. Maybe the "Detect Displays" will do it automagically for you.
As for the icons, check the settings in "Desktop". Or you can use the "Preferences" option in the menu to do all this in Cinnamon.