Is it normal that food gets stuck in the gaps that remained in between the porcelain veneers after one week?

It sounds like your veneers weren’t bonded very well or your teeth have moved.  
If the bite is putting pressure on the veneers, it may force the teeth to move.  it’s possible the veneers just weren’t made right.  
Well made and cemented veneers should feel natural and look great.  
In an advanced esthetic practice, they can do a ‘trial smile’ so that you can see and feel what your getting before the job is done. 

It is possible to have veneer material stick out over the natural teeth structure to create the esthetic appearance that you or your dentist is trying to achieve. See your dentist and see if this gap can be covered up with a new veneer or you may switch it to a crown. 

Hi:Unfortunately without photo it is difficult to give you accurate advice.  Please post photo of the area.  You should go back to your dentist and voice your concern.Best,Dr. Maddahi