It's a lot like yoga or self-disciplined sports. You always have to develop patience, inner mental strength, breathing technique through listening to yourself, feeling yourself, and a good vocalist, because you have to approach all that even with a mentor. I highly recommend Berklee Vocal for Performance with Donna McElroy DVD, and then some practice, and then some silence, and then some listening, and rinsing and repeating. When teaching yourself how to sing, another important thing to learn is how to sing with a chest voice.
Growth as a singer is almost certain to happen, but you have to be realistic and patient with yourself. Learning to sing on your own may require more work than working your voice with singing lessons or private singing tutorials. Which will make you tired of singing in general, and most likely will lead you to stop practicing altogether. I'd like to ask if you know any good singing classes that aren't zooming near Kyneton Australia.
To reach your full potential as a vocalist, you'll need to be able to switch between the head voice and the chest voice, using something known as a mixed voice. If you mean learning how the voice physically works and understanding the anatomy, physiology and physics behind it, or learning music theory skills with books, then yes, that is also possible, although it is probably quite difficult, time-consuming and possibly expensive if you want to buy textbooks and other materials. When you vocalize, utterance is important and each vocal coach will tell their students to look in the mirror when they sing to avoid taking wrong notes. If you mean learning to consistently produce beautiful and healthy sounds with your voice, while minimizing unhealthy or harmful habits, and learning to stylistically apply them to the repertoire that is appropriate for your voice and development.
Personally I have little talent for singing, but I managed to sing in a way that makes me sound like a talented singer. Learning to sing is not the same as talking, but self-taught singers can learn a lot from the mechanics of speech. That said, vibrato isn't something you should start learning right away; to learn a real vibrato, you'll need to develop proper breathing techniques. You may not think that you will be able to distinguish between these vibrato and genuine vibrato, but you will be surprised: a real vibrato is pleasant to the ear, while the effects of tremolo and oscillation sound unpleasant, even if you are not trained.
For example, when you sing a scale, you might want to work on briefly playing a note higher than you're comfortable with before going down the scale again. If you want to start researching some of the ways you can start learning to sing with vibrato, this video will teach you some exercises to use.