The implication in the movie is they are walking to Switzerland or Italy, either of which is, as you point out, geographically infeasible.
In reality, they walked to the local train station and traveled to Italy, and then to the United States via London.
But that doesn't make for as dramatic of a movie.
According to the website Sound-of-Music.com it was shot with a helicopter mounted camera.
The opening scene that became one of the most famous in film history was filmed on a mountain about 10 kilometers into Bavaria. The scene was shot from a helicopter and had to be perfectly timed, so one of the crew members hid in the bushes with a megaphone and ...
The Sound of Music is loosely based on the first part of the book, The Story of the Trapp Family Singers. In real life, the von Trapps' priest, the Reverend Franz Wasner, acted as their musical director for over 20 years, and the father of the family, Georg, was actually an active participant in the music rather than the strict and distant disciplinarian we ...
The movie, perhaps deliberately, mixed up its geography.
As you pointed out, Switerland is on the "wrong" side of Austria relative to Salzburg. The two "neutral" countries near Salzburg were Czechslovakia and Hungary.
But those countries soon fell into German "orbit" (Czechoslovakia by force, Hungary voluntarily). So the movie may have wanted to use ...
The distributor cap.
It was a commonplace trick at the time to disable a vehicle by removing the rotor arm from the distributor, but this small part would be harder to show on film.
The distributor cap is simple to unclip and remove - taking just seconds. It is also a clearly recognisable part.
Almost all movies derived from stage musicals will add at least one original song, the objective being to make it eligible for an Academy Award nomination for Best Original Score. In recent memory, Beauty and the Beast did this, as did Les Miserables and Into the Woods. The new Wicked movie will have original songs as well. It's actually difficult to find ...
Uncle Max is not actually a blood relative, merely a friend of their father's.
In this instance, the 'Uncle' title is an informal title for a close friend.
There's actually more information (that may or may not have any bearing on his role in the story) here: IMDb Bio.