MacBook Pro :: Time Machine Won't Back Up And Files Won't Open When Double Clicked

I have a 13in MacBook Pro Mid 2012 model with a 2.5 GHz Intel Core i5 processor and 4 GB 1600 MHz DDR3 memory. I've got it new in the summer of 2012, and haven't had any real problems until now. I have a 1TB Hitachi external hard drive with over 600GB left of storage. I'm running Yosemite. 

Lately, as in the past few weeks but more noticeably the past few days, I can't open files if I just double click on them from my desktop or from searching them outside of the application. For instance, if I click on a word document on my desktop, it will cause the work icon to bounce for a while, pretending to open, but it never does. If the application is already running, the file just won't open. If I search from the "open" selection within the application, it works fine. This is true for all of my Microsoft Office apps, Photoshop, Preview, iTunes, and everything in between, all of which I had never had a problem with before. 

Next, anytime I try to backup my system using Time Machine, it simply shows the "Preparing Backup" status and never starts. I've had the hard drive and used it as a Time Machine since I got the computer, and have had zero problems at all. 

I've tried CleanMyMac2, Memory Clean, and I've always kept my Mac very clean and organized, as in no duplicate files, moving my biggest files onto my hard drive, and deleting any of my unnecessary files.  I know I don't have a ton of RAM left, but I'm honestly not completely sure what to do about that, as this model apparently doesn't have RAM updates available.  

Info:
MacBook Pro (13-inch Mid 2012), OS X Yosemite (10.10.1)