If using Glmm with Gamma distribution do i need to transform my data to be between 0 and 1? When creating a Glmm with Gamma distribution do I need to transform my response variable data to be between 0 and 1?
 A: No, you do not need to transform your response variable, $\mathbf{y}$ to $[0, 1]$. The only condition to use the Gamma family is that $\mathbf{y} \in (0, \infty)$.  You do not mention what software you are using, but here is a little example in R.
## simulate some data ##
# set seed
set.seed(10)
# random effect
u <- rep(rnorm(500, 0, .1), each = 25)
# predictor
x <- rnorm(500 * 25, 0, .1)

# outcome
y <- rgamma(500 * 25, 1/(1 + u + x))

# id
id <- factor(rep(1:500, each = 25))

Trivial case with just one predictor and a random intercept, but we can now fit the model with glmer() from the lme4 package.
## load lme4 and fit model ##
require(lme4)
(m <- glmer(y ~ x + (1 | id), family = Gamma))

Generalized linear mixed model fit by maximum likelihood ['glmerMod']
 Family: Gamma ( inverse )
Formula: y ~ x + (1 | id) 

      AIC       BIC    logLik  deviance 
 25558.46  25580.76 -12776.23  25552.46 

Random effects:
 Groups Name        Variance Std.Dev.
 id     (Intercept) 0.009809 0.09904 
Number of obs: 12500, groups: id, 500

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 0.999305   0.009985  100.08   <2e-16 ***
x           0.942499   0.086799   10.86   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
  (Intr)
x 0.176 

And you can see we recover our parameters fairly well.  The SD of the random effect is $.099$, close to the $.1$ used for simulation, and the intercept and slope of $x$ were both simulated as $1$, which is essentially what glmer() estimated.
