Unless you have theory for it, I wouldn't get rid of say a quadratic growth factor if it is insignificant in one latent class. Just report this.
Your last question takes a latent class course to go through well - you should study the literature and our videos. Briefly, take for example the intercept growth factor mean [i]. This influences the probability of say a binary item at the time point where the time score is zero. It does so via the logit as