Multi point door lock security and can I use wood screws near it?
The "no screw" locations will vary from lock to lock.  The typical "multi-point lock" has 3 latches that interface with the side of the door frame like this:



As you can see, screwing anywhere at the top or bottom of the door should be fine.

If you do have a type of lock with bolts that go into the header and door sill, I would expect the "boxes" to be smaller, but still present in the area of the bolts.  Measure from the door frame to the far side of the bolt, and add 20-30mm to that for your no-screw zone.  That should put you beyond any hardware and into good solid wood.

Of course, if you can find a manufacturer for your lock set, Google it up and see if you can get a picture or installation instructions so you know exactly what to avoid.