MacBook Pro randomly freezes, can't do anything
I had the same exact problems with my 2010 iMac 21.5 running 10.10.4. 

Open up Activity Monitor and have it run behind you to check memory pressures and CPU usage. My guess would be your RAM is overloaded, so it cannot make any changes to your system. 

Downloading the trial version of CleanMyMac 3 lets you have a nice little memory checker in your status bar. I would recommend (since you cannot upgrade RAM) look for software to optimize your memory usage or alert you when you use too much so you can close needed applications. The internet is full of guides to help lower RAM usage.

Hope that helps