1. No, not really.
2."The car's gas cap is off." you don't need to include tank because it's common knowledge a gas cap is on a gas tank so people don't say it and you might sound weird if you do.
3."My's phone's color is black." or "The color of my phone is black." would also be acceptable if this is in reply to a question most people would just reply black because both people already know we are talking about your phone.
4."Neither dogs' bark is the same" "This isn't either of your's car" or "This isn't either of your guys' car" it's okay to represent girls with this the word 'guys' as long as your familiar with them kind of like 'amigos' in Spanish if it's a mixed group of girls and guys