I have also been asked on various occasions if I have a dance background, I have to laugh because I was the least physically inclined teen ever growing up. I didn't even play sports. However, I do credit a lot of my body awareness and even clean lines to a yoga background. A great yoga teacher I had in college really drilled her students to use proper form and I think this really helped me in the long run in areas I never imagined: Pole and aerial dance!
Proper yoga form, I think, that translates into dance/pole includes:
*Stacking joints: i.e. keeping elbows in line with wrists and knees in line with ankles. Keeping this in mind in extensions pretty much guarantees straight lines.
*Energy in hands and feet: While yoga doesn't push pointed toes like we do in pole, it does encourage us to keep energy in our entire body, from the tip top of your head to your toes. This is true for dancing, too. Often you can see pretty straight legs or arms with limp hands and feet. Visualize energy flowing straight through your arms and legs and shooting out of your hands and feet. This helps avoid the hands/feet "turning inward" like you described. On a side note: Remember "pointing your toes" is actually more than your toes working, you have to really push through your entire foot and ankle to create a flat line down your shin through the top of your foot and toes.
*Squared hips and posture: Being aware of your hips is helpful in your lines and posture. Keeping them straight and squared allows you to focus on your core and not "dump" into your lower back. Also, chin up and shoulders back, and remember that energy coming from the top of your head! Like there is a string running through your spine and pulling up at the top of your head.
Seems like a lot to focus on at once, but body awareness in these areas really helps with lines, posture, and even keeps your joints/bones safe while dancing!