DirectX is included by default as part of the Windows 7 operating system. As such, you shouldn't ever really need to "install", "uninstall", or "repair" DirectX as a software program, per se. However, sometimes operating system files become damaged or corrupt. You could try running a system file checker scan from an elevated command prompt (option two.) If any problems are found, run the scan 3 times and reboot the computer after each scan.
SFC /SCANNOW Command - System File Checker
Microsoft frequently releases updated versions of DirectX and installing the latest updates may be the fix to a DirectX problem you're having or may give performance increases in your games and graphics programs. Normally that's done thorugh Windows Updates, but you could search for the latest version on Microsoft's website.
Typically, the DirectX End-User Runtime Web Installer
link will be your best option since it's the latest release and only installs the DirectX files you are missing. Some users prefer to download and install the entire DirectX package by choosing the DirectX End-User Runtimes (MONTH YEAR)
link with the latest month and year available. Note:
The DirectX SDK
download options are NOT
Search results - Microsoft Download Center
After any installs restart your computer, even if you're not prompted to do so. After restarting your computer, test to see if updating to the latest version of DirectX corrected the problems you were having.
Assuming you do have FTL installed, it wouldn't hurt to tell AVG to ignore it.
As far as the AMD drivers, you could always try an older driver to see how it performs. Sometimes "newest" doesn't always mean "best" when it comes to drivers.
Strongly suggest making a restore point before installing DirectX End-User Runtime Installers or any drivers. Better yet, make a system image.
System Restore Point - Create