I don't know anything about computers to be honest. I have an AMD Radeon HD 8570D Graphics card. What is dxdiag?
Dxdiag is just the information panel on your graphics drivers. Type in "dxdiag" in your Start bar or search for "Run" and type "dxdiag" into that. You'll get a window with the version of DirectX you're running at the bottom. Given a Radeon HD 8570D you should be running DX11 anyway.
Only way to know if the 64-bit client works is to run it. For that you'll have to manually locate it in the ESO folder, which should be "C:\Program Files (x86)\Zenimax Online\The Elder Scrolls Online EU\game\client" and the launcher to use is eso64.exe. You can also right-click it and use "Send To" to create a shortcut on Desktop.