Stand on your toes and stretch your entire body for a few seconds. Then return to its normal position and extend it again two or three times. Like any musical skill, it requires practice, but yes, it can be learned. I'm not mainly a vocalist (I'm a guitarist who starts singing from time to time), so I can't give any recourse.
Practice hitting the notes with the attached vellum (that is, the flap that closes the oral cavity when you make the ng sound) and then unhook the middle note. It's easier to be precise with the vellum attached, although I don't know why. It is no coincidence that every professional singer separates a large part of his singing studio to train his breathing. Patients with brain damage may experience loss of ability to produce musical sounds while still speaking, just as aphasics selectively lose speech, but sometimes they can continue to sing.
There is a way to improve singing without a teacher, but there will come a time when you will need someone else's ears and experience to help you. While focusing on this is a little later, since you say you want to work on fundamental things like increasing pitch accuracy, I don't think it's too early to challenge the way you perceive your own voice and try not to force any expectations on it. Now I can sing something basic, my vibrato starts to come in slowly, I learned to hold my breath and I even learned to fry screams and sing the basic throat (kargyraa). You can sing with any voice and ability you have, but the goal of the lessons is to train you to condition your anatomy and reflexes so that they work more accurately and efficiently.
OP, this is a perfect example of why you need to see a teacher who really understands singing as a functional process. There was a lot more to singing than I knew (I thought I just needed to play the right note with a good tone. Record yourself, sing songs you know to improve your stay in the field, try to walk to the rhythm of the music to keep you on time, try to imitate the different singers you like. If you can sing in tone, that's a good start, & will be able to improve the strength of your voice with different warm ups & exercises.
Try to imagine if your feeling of not being able to sing a song by your idols convincingly is not due to lack of originality. I would record myself and find out what notes I couldn't sing and then highlight them to fix those individual notes. People with excellent ears often sing out of tune, and it is not related to their ability to match the tone, but it is just a vocal problem that they need to address. I like doing karaoke a lot, since it's really the only moment, apart from my classes, when I can sing with a microphone and it's very easy to get caught up in the moment and sing louder than necessary.
Basically, what I've found works for me is that it's great to get feedback from my voice teacher, but even she might not have the right vocabulary or description right now and diving into the topic has helped me collect different descriptions and improve possibly faster than I could with just one output of learning.