What is the best approach to improve my sound (tonguing, getting more volume, play by ear, improvising/soloing)
(Has been playing 10 years, practices three days a week)
(Has not yet tried to learn anything by ear)
Not an especially specific question, but it basically has a straightforward answer.
First thing would be to practice more. If you’re aware of your sound, it should get a little bit better every time you play.
Practicing three days a week means you’re practicing less than half of the days in a week.
Each day you don’t practice, you get a little bit worse.
Volume depends a bit on which reed and mouthpiece you use, but also on your physical condition.
To get better at learning music by ear you have to start learning music by ear. To do that, I would recommend starting with simple melodies that are played slowly. Learning Taps by ear on saxophone could be a good start.
Pretty much anything you do on saxophone will get better by practicing more.