Is it possible to design headless tests with JMeter/Selenium? (and Docker)
JMeter supports headless operation, in fact it's even the recommended mode for best load testing results. From Non-GUI Mode (Command Line mode):


  For load testing, you must run JMeter in this mode (Without the GUI)
  to get the optimal results from it. To do so, use the following
  command options:
  
  -n
      This specifies JMeter is to run in non-gui mode


As for Selenium, things are a bit debatable, the Does Selenium support headless browser testing? SO post is probably interesting, personally I find Ross Patterson's and General Redneck's answers most useful - basically recommending the use of a virtual X server (Xvfb, for example) instead of a headless browser.

A nice related post: How To Run Your Tests Headlessly with Xvfb.