It seems more complicated than the software route. What if after doing this, the sound that the ZOOM gives to my teacher is crappy (low quality, delayed, choppy, cuts) again?
Or is doing it this way (mixer) ensure CD crystal stereo quality like sound to zoom meeting participants?
The microphone, mixer and audio interface will solve NONE of these problems. These are all the results of the Internet being packet switching rather than circuit switching (long story, search on wikipedia if you care about the details). In packet switching "perfect" video/audio calls are impossible. In short, each "piece" of your video and audio may arrive to the destination in any order, even after a long time. Or it may never arrive. Hence the cuts, the delay, the latency. That's just the way it is. Video/audio calls are made possible only "approximately" with a "firehose" approach: let's use a firehose when a 1/8" pipe would suffice, and hope that the extra volume will mitigate the problem caused by the packet switching.
To further mitigate this problem, if both you and your teacher have MIDI-enabled instruments, you can try InternetMIDI (Google it, it's on sale right now, but there is a demo version a little bit hidden in their website). That will send only MIDI signals (rather than audio) to your teacher. Since MIDI is much less data volume than audio/video, this makes the "firehose" approach possibly better: now you'd need a hairline pipe and instead you are using the firehose. In this condition the packet reordering, packet loss and other internet downsides should become less severe. Note I wrote "should" not "will for sure". You still need the audio/video conference software, but you'd use that just for the voice part of the lesson, not for the "playing the instrument". Disclaimer: I haven't tested this software (yet) and I plan to do so -- I have no interest in that company.
One other thing that you must do is checking everything you can regarding your internet connection, to make sure it's in the best situation. For example, microwave ovens (even in other rooms or nearby apartments) interfere with some channels of WiFi. You have to make sure you have no such oven on while using those channels -- or switch to different channels. Your teacher needs to do the same. And this is just an example, the full list of things to consider is two page long.... I am mentioning this example since it's less known than "make sure you are not distant from the wireless router, and you do not have too many routers connected to each other making additional hops, and make sure other family members are not watching netflix during your music lesson and plenty of other "obvious" things. I know, it's a pain.....
Then it comes your internet vendor... Sadly they hide all these things by saying their internet is "fast internet" and at most provide a bandwidth number calling it "speed" (which is plain wrong, the "latency" if anything is the speed). Google these things too if you want to educate yourself on these other aspects, in the end all related to packet switching.
