Can we use 0patch in parallel to Windows Extended Security Updates?

Yes you can. Obviously our post-EOS Windows 10, Windows 7, Windows Server 2012 or Windows Server 2008 R2 micropatches won't be applied (or needed) on a computer with ESUs installed, but our micropatches for other software products will still get applied. In addition, should we issue a micropatch for a published 0day before an official fix is available from Microsoft, we will make one for both fully updated Windows systems without ESUs and Windows with ESUs installed.