Answer to question of sufficient air
The situation of running out of air is no different than a student violinist running out of bow length. True there are situations where there is not enough bellows length but every study in the book is worked out carefully to avoid that if one follows the arrangements as written.
Generally the reason one runs out of air is because one is searching for the next note while pressing the preceding note and using up air. The solution is not to search for the note. This is in fact the whole point of the lesson. This is so important that I need to say it again. The solution is not to search for the next note. If your fingers are in position for the entire phrase before you start playing the phrase it is only a question of playing them in the correct sequence. In the case of Shoes and Stocking, it means placing the fingers, for example in first measure, on G, B, C, and D. Try playing all four notes at once. Now put the fingers in the same position but don’t press the buttons. Try now to play the buttons separately in the sequence G B CC D. If you are still have air issues, play G- release, B – release, C –release and so on the notes come out short. You can practice the phrase with very short notes (staccato) and then try to play the phrase perfectly smoothly (legato). Then try to play as loud as you can. Then try to play as soft as you can and as fast as you can. The fastest you can play it is almost like playing all the notes simultaneously as described above. Each phrase should be treated as such.
More importantly this first lesson demonstrates the concept of visualizing the phrase first in your brain, placing the fingers in the correct position and then playing the sequence in the proper order –preparing the hand. Every phrase should be approached in this manner. It is really hard to do and takes constant practice, as we all tend to want to play the music note to note. This later technique however is a very inefficient learning process, much harder to play rapidly and harder to memorize. You are not the lone ranger, everyone experiences this tendency, myself included. Nevertheless this is the guiding principle in the book and I commend you for spending the time already to really explore this approach. It is important to make this process a habit. You will find that after the first 8 lessons, you will be miles ahead of more experienced player that search note by note.
As to the second question of playing the last measure of 1/16th notes where there is change in bellow direction, the same principle of preparing the hand applies. In the reverse fingering page 35 measure 4: the first notes are in the closing position – D, E, D, C, B, and G. All 5 fingers can be placed on this phrase. Push them simultaneously. The second part is in the opening position and the notes A, F#, G are all on the left hand. Play this note simultaneously. Now go back and forth between the 2 positions, playing the phrases as blocks of sound until the movement is seamless. Once you can do this with an automatic sense, you can separate the notes and play them as short notes pressing and releasing each one in the correct sequence.
Finally, there are times after long phrases where the simultaneous use of note and air are used in the following short phrase to reposition the bellows. It is useful and similar to the violinist moving his bow rapidly on a short phrase to prepare for the next phrase, which requires a full bow.