Is it normal to submit an abstract to a conference when the research is NOT completed?
Is it normal to submit an abstract to a conference when the research
  is NOT completed?


Sure.  There are plenty of fields where the purpose of a conference is to discuss research that is "still cooking."  In fact, many journal publications can be viewed as interim reports on larger research programs that are still in progress.

You might use this opportunity to set a goal for (roughly) the piece of your thesis you want to have done by the date of the conference.  It's ok if that piece is relatively small, and nobody at the conference will hold you strictly to what you say in the abstract.

In fact, some people submit abstracts on one thing and then talk about something entirely different... I won't advocate that behavior as an intentional strategy, but I will say that many people (myself included) prefer a great talk to exacting consistency with the abstract.