Galaxy S5's screen only turns on after multiple presses, and the screen has these weird lines show up when turning off and thanks for reading this. So I've had an S5 for just over a year now. As it has an AMOLED screen, when you turn the brightness all the way down, the screen will flicker a yellow-green. This happened whenever the screen would dim on standby, and it seemed that it was normal. However, now, when I power it off, the screen does the green flicker when it's fading out. This did not happen before. 

On top of this, sometimes the screen simply will not turn on. The phone is on, the lights are on, but I'll press the power button, and nothing will happen. I'll keep pressing it, and eventually it will turn on, but this could be part of an underlying issue. If anyone has any ideas, please do tell me.

Also, smaller issue: woke up one morning, and a notification came up at 3 AM saying that I was running out of storage space. Is my phone trying to kill itself?
The first part of this screams either a broken screen or much more likely, a broken screen driver (Software being corrupted). Backup your data and factory reset the device. Do not recover using the backup and just move your contacts back and pictures. You can always reinstall apps. If that doesn't fix it, you will likely need to replace the device or flash the stock software again.