Hey Oliver,
I think I know whats going on here. after you drop your footage into a new comp, there is a little button at the bottom of the video window. It’s just to the right of the “1 view” dropdown arrow, it’s a rectangle with a line and an arrow point on each end above it. If you hover over it with your mouse it’s called “Toggle pixel aspect ratio correction” Click that and see if it makes your comp appear full wide (16.9).
As far as rendering out, click on the word “lossless” then I select “stretch” then “HDTV 1080 30Fps”, you’ll have to match the same as the footage you shot unless you’re up or down converting. Don’t forget to click the checkmark on your audio too if you have audio.