How long does it take to see new growth from braids I forgot?

I got braids Friday and I'm growing it out some more and when will they actually get more looser? Will it take weeks or months....also is it ok to wash them in the shower once a week? I washed them in the shower yesterday....will they frizz? Also they say to dilute with shampoo and water but I work that it won't get it clean enough....I mean can it still grow even if u didn't get all the dirt? Sorry but i'm a big worrier when it comes to growing longer hair