iMovie, either on the iPhone or a Mac should do what your grandson wants to do. And best of all, it's free and you probably already have it.
I have an older version of iMovie (V7.1.4) but it requires iDVD to burn a disk, which was part of the now discontinued iLife. There is a downloadable newer version (V9.0.9) which will work with my OS but, as joemike points out, it won't burn to DVD - and that is a showstopper.
Do you have a CD/DVD drive for your Mac…
Yes. I have an Apple Superdrive that I use to make CDs for playing in the car.
2. Is there any software available that I could use to make portrait-shot videos adapted to 16:9 without everyone looking fat and wide?
iMovie might also accomplish what you want in your #2, I just don't know.
I don’t know either but I somehow doubt it.