How to remedy an unusable MacBook Air?

Question

Hello everyone!
I am writing to you about my wife's MacBook Air. It has sadly become what seems like the most unusable notebook on the planet.
I am relatively good with computers and have endlessly searched for ways to improve its performance but have come up dry. I've tried all the little things like reducing transparency and cleaning up unused files. At this point I feel as if I've tried it all.
It will beachball and hang at the smallest task. For example, it takes 5-10 minutes to open Firefox, and an additional 5-10 minutes for Firefox to be usable. Virtually every application behaves that way and it is driving us insane. My wife uses this notebook for everything and we have to get it fixed.
It was barely a year old when I bought it, with Mountain Lion installed. It ran like a dream. But as soon as I upgraded to Mavericks it started to go downhill. Now with Yosemite it's becoming even worse as time goes on. I'm debating on simply rolling back to Mountain Lion to see if that does the trick. We are so frustrated with this thing.
I've attached an EtreCheck report for you, I hope it gives you some usable information!
I appreciate your time in advance.
EtreCheck version: 2.1.8 (121)
Report generated February 10, 2015 at 11:28:25 PM EST
Download EtreCheck from http://etresoft.com/etrecheck
Click the [Click for support] links for help with non-Apple products.
Click the [Click for details] links for more information about that line.
Hardware Information: ℹ️
    MacBook Air (Mid 2009) (Technical Specifications)
    MacBook Air - model: MacBookAir2,1
    1 1.86 GHz Intel Core 2 Duo CPU: 2-core
    2 GB RAM Not upgradeable
        BANK 0/BuiltIn0
            1 GB DDR3 1067 MHz ok
        BANK 0/BuiltIn1
            1 GB DDR3 1067 MHz ok
    Bluetooth: Old - Handoff/Airdrop2 not supported
    Wireless:  en0: 802.11 a/b/g/n
    Battery Health: Normal - Cycle count 151
Video Information: ℹ️
    NVIDIA GeForce 9400M - VRAM: 256 MB
        Color LCD 1280 x 800
System Software: ℹ️
    OS X 10.10.1 (14B25) - Time since boot: 0:36:5
Disk Information: ℹ️
    SAMSUNG HS12UHE disk0 : (120.03 GB)
        EFI (disk0s1) <not mounted> : 210 MB
        Macintosh HD (disk0s2) / : 119.17 GB (49.66 GB free)
        Recovery HD (disk0s3) <not mounted>  [Recovery]: 650 MB
USB Information: ℹ️
    Apple Inc. Built-in iSight
    Apple Inc. Apple Internal Keyboard / Trackpad
    Apple Computer, Inc. IR Receiver
    Apple Inc. BRCM2046 Hub
        Apple Inc. Bluetooth USB Host Controller
Gatekeeper: ℹ️
    Mac App Store and identified developers
Kernel Extensions: ℹ️
        /Library/Extensions
    [not loaded]    org.virtualbox.kext.VBoxDrv (4.2.16) [Click for support]
    [not loaded]    org.virtualbox.kext.VBoxNetAdp (4.2.16) [Click for support]
    [not loaded]    org.virtualbox.kext.VBoxNetFlt (4.2.16) [Click for support]
    [not loaded]    org.virtualbox.kext.VBoxUSB (4.2.16) [Click for support]
        /System/Library/Extensions
    [not loaded]    com.sony.driver.prs (1.0.1d1) [Click for support]
Launch Daemons: ℹ️
    [loaded]    com.adobe.fpsaud.plist [Click for support]
    [loaded]    com.adobe.SwitchBoard.plist [Click for support]
    [loaded]    com.barebones.textwrangler.plist [Click for support]
    [loaded]    com.bombich.ccc.plist [Click for support]
    [loaded]    com.microsoft.office.licensing.helper.plist [Click for support]
User Launch Agents: ℹ️
    [loaded]    com.macpaw.CleanMyMac2Helper.diskSpaceWatcher.plist [Click for support]
User Login Items: ℹ️
    iTunesHelper    Application Hidden (/Applications/iTunes.app/Contents/MacOS/iTunesHelper.app)
Internet Plug-ins: ℹ️
    JavaAppletPlugin: Version: 15.0.0 - SDK 10.10 Check version
    FlashPlayer-10.6: Version: 16.0.0.287 - SDK 10.6 [Click for support]
    Default Browser: Version: 600 - SDK 10.10
    Flash Player: Version: 16.0.0.287 - SDK 10.6 Outdated! Update
    AdobePDFViewer: Version: 10.0.0 [Click for support]
    QuickTime Plugin: Version: 7.7.3
    OfficeLiveBrowserPlugin: Version: 12.2.3 [Click for support]
    Google Earth Web Plug-in: Version: 6.0 [Click for support]
    Silverlight: Version: 5.1.30317.0 - SDK 10.6 [Click for support]
    DirectorShockwave: Version: 11.5.2r602 [Click for support]
    iPhotoPhotocast: Version: 7.0 - SDK 10.7
3rd Party Preference Panes: ℹ️
    RCDefaultApp
    Flash Player  [Click for support]
    Perian  [Click for support]
Time Machine: ℹ️
    Mobile backups: OFF
    Auto backup: NO - Auto backup turned off
    Volumes being backed up:
        Macintosh HD: Disk size: 119.17 GB Disk used: 69.51 GB
    Destinations:
        Sueann's Backup Drive [Local]
        Total size: 152.43 GB
        Total number of backups: 1
        Oldest backup: 2014-12-26 07:04:47 +0000
        Last backup: 2014-12-26 07:04:47 +0000
        Size of backup disk: Too small
            Backup size 152.43 GB < (Disk used 69.51 GB X 3)
        Josh's Time Capsule [Network]
        Total size: 2.00 TB
        Total number of backups: 10
        Oldest backup: 2014-05-17 08:30:01 +0000
        Last backup: 2015-02-11 03:06:36 +0000
        Size of backup disk: Excellent
            Backup size 2.00 TB > (Disk size 119.17 GB X 3)
Top Processes by CPU: ℹ️
         9%    WindowServer
         1%    sysmond
         1%    AppleSpell
         0%    Activity Monitor
         0%    Dock
Top Processes by Memory: ℹ️
    301 MB    firefox
    75 MB    com.apple.preferences.parentalcontrols.remoteservice
    75 MB    com.apple.preferences.users.remoteservice
    60 MB    WindowServer
    56 MB    Finder
Virtual Memory Information: ℹ️
    50 MB    Free RAM
    707 MB    Active RAM
    674 MB    Inactive RAM
    283 MB    Wired RAM
    2.90 GB    Page-ins
    59 MB    Page-outs
Diagnostics Information: ℹ️
    Feb 10, 2015, 10:45:12 PM    Self test - passed
    Feb 10, 2015, 01:38:55 PM    /Library/Logs/DiagnosticReports/softwareupdated_2015-02-10-133855_[redacted].cp u_resource.diag [Click for details]

Answer 1

When you see a beachball cursor or the slowness is especially bad, note the exact time: hour, minute, second.  
These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.
Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.
Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.