But in Portuguese, "cada dia" is a little more specific, you can totally say - Nas férias, eu leio cada dia. A native speaker would understand you, but maybe isn't the best way to express yourself in this case. Nas férias eu leio todo dia. No meu trabalho, cada dia eu encontro um prolema diferente. That's fit perfect in Portuguese. I don't know if this would fit in English, but the translation would be - on my job, each day I find a different problem. Eu vou para a academia todos os dias, e a cada dia que passa, eu fico mais forte. I go to the gym everyday, and each day I get stronger.

Yes, you got it exactly right. And it's normal to mix both of the terms, like : Meu nome é Pedro, e eu estudo inglês todos os dias, o dia inteiro. My name is Pedro, and I study English everyday, all day long.