Herarchical three-level (Multilevel) generalized linear logistic regression repeated measure with nesting/crossing using glmer in R

#1
HLM.png
I have been trying to find out the most adequate glmer formula for my data but I found no example that reflects my specific structure as illustrated above.
My data is dichotomous [correct/incorrect (0,1)] for vocabulary tests:
So here is what I have:
Subjects
Response
as DV
Time: Pretest,Posttest
Group: Control, Treatment
Words: 20 items tested
7 additional fixed effects
I want to test the significance of change over the 2 time points.
Problem:
I want to make sure that the comparison analysis for groups is based on individual score change on each 20 item rather than comparing individual or group scores average.
Potential Model
I assume that this model is a :
hierarchical (Multilevel) generalized linear repeated measure logistic regression model
mod1 <- glmer(Response ~ Group*Time + (1|Group: Word) + (1|Subject), data= vocabDat, family='binomial')
  1. How far is my model formula correct and reflects my aims of hypothesis testing?
  2. Is this a Growth Curve Analysis ?
  3. Is it true that Rasch is better model for my data analysis?