Q.magnolia varieties
1- Which magnolia variety has the smallest flower
2- what kind of magnolia is shown in the picture below

Certified GKH Gardening Expert
Magnolia x soulangeana 'Lilliputian' is reported to be the smallest variety, and thus has the smallest flower. This would be the most suitable variety to apply Bonsai methods to.
The variety in the photo will be known to the person who planted it. I can get you close and say that it is most likely Magnolia soulangeana, but giving you the exact cultivar is probably a long shot.
This article will give you more information on Saucer Magnolias: https://www.gardeningknowhow.com/ornamental/trees/magnolia/saucer-magnolia-trees.htm