If one takes off his teffilin during Shacharit because he needs to use the bathroom or some other reason, does he have to say the bracha again when he puts it back on?

Yes, since you can’t bring tefilin in the bathroom it’s considered to be a hefsek.
What about his tallit?
No.
Kavod HaRav, is there a difference between using the bathroom for ketanim and gedolim? (regarding a new bracha)
No, once you enter the bathroom, you are required to say a new bracha