iMac tries to quit programs and restart whenever it puts the display to sleep

Hi everyone!

I have a late 2008 iMac all-in-one with the most recent Yosemite OSX 10.10.3 (14D136). This problem has been around ever since I updated to Yosemite for the first time. I use this computer as my desktop computer and as a server for various projects. I need the computer to stay on andall programs must stay open. I would also like the monitor to be able to go to sleep so I don't wear it out. No matter what settings I choose, it seems like, it tries to quit all applications and shutdown when I leave it alone. I can't tell what is triggering this. Here are my settings:

ENERGY SAVER:

Computer sleep: never
Display sleep: ~20min

Do I need to set display sleep to "never" too? Won't that ruin my monitor? I want everything to stay open and running forever, but the screen should turn off after ~20min. What am I doing wrong? Why does it start quitting everything and shutting down?

GENERAL:

In the "general" control panel it is set to "ask to keep changes." This is seemly unrelated, but often when I come back and if the screen is dark, when I move the mouse there is a dialogue saying it could not shut down because some app was asking about saving changes. Though, just as often, there are apps that closed successfully ... much to my dismay ... so having this on is my kludgey way of stopping the shutdown.

SECURITY & PRIVACY:

Could this be the issue? I even turned off the login password. I'd rather have it on, but I assume this isn't possible if I want all programs to keep running.

DESKTOP & SCREEN SAVER:

The screen saver is set to start after "never" now, but I've tried turning it on too.

I tried looking for similar issues and found mostly people who were having boot problems, or the computer shutting down with no warning. This happens to me only when the computer is left without mouse or keyboard input for several minutes. Then, instead of shutting the display off and continuing to run the programs SOMETHING in my system triggers it to shut down and it starts closing all programs. Often it gets stuck while doing this but the damage is done either way.

How do I keep my programs running? Thanks in advance to those who take the time to help me out with this issue!
😊