Hello Andreas
You got a nice website layout and nice way to show 2 different slide shows in one. eg. slides + design process.
To get an internship, you need to show more sketching pages and different styles, which is are missing !
Try not to repeat lot of renders/photographs again and again, because its time consuming and telling the same thing. Try to pick the best view which explains your idea in few slides.
Why not to synthesis your text in few lines which tells the summary/brief of the project, then there could be place for more text to read if interested.
The desk lamp idea is really clever. Why not to think of different arrangements with different accessories, wall hanging, pendent lamp, floor lamp…
Goodluck !