Re: while followed by verb+ing after Future simple
I think it's because the bath starts, then the reading begins, then you put the book down, and then you finish your bath. So "read while I am taking a bath" sounds okay (to me).
To say "take a bath while reading" makes it sound like you have your nose in your book as you turn on the taps, get undressed, and so on.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.