I was told that as foreigner to just forget it and use them interchangeably, since only a person with a very deep understanding of the language (a native speaker) would know. It's just so subtle and the explanations for them are just so weird and difficult to truly understand.

they are both same meaning, but I can find only small difference between these two. 

하며(it sounds like doing something and another thing at the same time, it presents now or in general use) 

하면서(it is sounds more representable and current movement than 하며, exercising the 'movement') 

And also, you can translate this sentence '한국말은 어렵기 때문에 하루에 적어도 3시간씩은 공부해야 하며 매일 공부해야 합니다.' as 'Korean language is difficut to learn so it has to be studied at least 3 hours everyday'

Because studing korean langauge is so hard, I have to study it for 3 hours in each day at least and study it everyday

basically, both are same meaning but different a little

하며 (do something and another thing at the same time or it just means 'and')

하면서 (do something and another thing at the same time)