Let's see:
Helix Antenne für Rundumempfang <- No, will not work. The price for one helix antenna is 1.5 times than the whole GPS-module.
Präzise 3D Geschwindigkeit <- This AND ground speed should be possible
Höhenmessung <- Shold be ok, needs to be relative.
Entfernung <- From what? Start point? Should be possible
Zurückgelegte Strecke <- This might be hard but will try
Geokoordinaten <- Of course.
Let's remember few things:
Arduino has little memory, we need to keep it simple. Also we are not making a "full competitor" for commercial solutions like Jetimodel MGPS or Powerbox GPS II. We are doing simple, affordable and easy to do DIY-solution. The helix antenna will raise the price of components too close the commercial solutions. There is nothing stopping for you to use it of course but in the reference-model it will not come.
Things I will try to add is direction as compass heading and time in local timeone. (Time in your own timezone is actually not easy it seems, if even possible in arduino pro mini)