Problems freezing after update to Mavericks 10.9.5

Question

I have a late 2011 Macbook Pro. all was fine until i clicked the button to update to Mavericks 10.9.5 (and I think there was another update too). Everything froze, the touchpad didn't work,.. nothing. Force quit did nothing. I closed lid - but later when I lifted it, it was all still frozen and I resorted to pressing and holding the on/off button. 
I've spent the last 24 hours trying different things - sometimes when it freezes, the laptop seems to think the edge of the screen is in the middle (i.e. keep taking the mouse left and it appears on the right of the screen), and also I am getting funny lines and dots on the screen (is it possible it's my graphics??) and the cursor changes to a funny vertical dotted line.
I tried starting it in safe mode - it got to the log in screen with loads of lines etc. on the screen, but I persevered as I had heard it would produce diagnostics.... anyway I ended up with a blue screen with black lines down it. Eventually I pressed the on/off button again.... so safe mode is not working... (I think.. unless I didn't wait long enough?)
As suggested on here, I went into the library and have now dragged the caches folder onto the desktop, and I am waiting to see if my laptop freezes again. This appears to have copied the folder onto my desktop, rather than moved it - is that right?
Today I have also removed 300GB of photos, as I was down to my last 19GB - just in case that was the problem, but it has frozen since, so I'm guessing not. I have 16GB RAM so that shouldn't be a problem.
I'm fairly new to Mac. I haven't encountered any error codes, just screen freezes and odd graphics. I haven't been able to find where the diagnostics are to run. When it freezes, it gets very hot, so I have been pressing the on/off button and letting it cool off.
I'm still awaiting to see if it happens again, but I wondered has anyone else experienced anything similar or does anyone have any advice. Any advice gratefully received!

Answer 1

Boot into the Recovery Drive by holding down Command R when restarting.
Run Repair Drive and Repair Permissions using Disk Utility in Recovery.
Restart and run the combo updater.
OS X Mavericks 10.9.5 Update (Combo)
http://support.apple.com/kb/DL1760
However, you might need to reinstall OS X in the Recovery Drive. This process should not damage your data but it's always advised that you backup first.
If you don't have a clone backup it's time to start. Just like a seat belt and an air bag protect you in different ways when driving, you need both Time Machine and a clone for full protection.
Both of these applications can be used to create a clone. You will need an external drive to backup your data.
SuperDuper! http://www.shirt-pocket.com/
CCC http://www.bombich.com/download.html
Free space: It suggested you have a minimum of 10% free but this can vary depending on the size of the drive. When you get below 10GB free you need to start moving files off the drive.
You can keep your iPhoto and iTunes Libraries on an external drive. Hold down the option key when launching the app to point to the new library location.