Understanding different (residual) output for glmer.nb vs glmmPQL

I am currently trying to understand the different output I receive when 
fitting a negative binomial mixed-effects model with both glmer.nb and 
glmmPQL.

I run the first via

glmer_nb = glmer.nb(outcome~1+x+y+(1|subject),data=data)

and the second via

glm_nb <- glm.nb(outcome~1+x+y, data = data)
theta = theta of glm_nb1 (e.g, in my case 0.97)
glmm_pql = glmmPQL(outcome~1+x+y, random=list(~1|subject),data=data, 
family = negative.binomial(theta = 0.97 , link = log))

For the glmer_nb model I receive multiple no convergence warnings:

In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
Model is nearly unidentifiable: very large eigenvalue
  - Rescale variables?Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
Model failed to converge with max|grad| = 0.0010975 (tol = 0.001, 
component 1)Warning message:

The glmm_pql runs fine (much faster as well)

In general, the coefficients are very similar. However, when looking at 
the residuals I can identify vast differences.

The residual diagnostics can be seen here:

http://imgur.com/a/MhZRu

Please enlarge the pngs to properly see them.

http://imgur.com/pdtVumg shows fitted vs. residuals for glm_nb
http://imgur.com/B0Qp6g9 shows qqnorm residuals for glm_nb
http://imgur.com/OVObgCz shows a qqplot based on random variates for a 
nb distr derived as follows:

getME(glmer_nb, "glmer.nb.theta")
10.0560436934476
nbquant<-rnbinom(n=length(data$outcome), size=10, mu=mean(data$size))
qqplot(nbquant,resid(glmer_nb))

http://imgur.com/ByUKR5b shows fitted vs. residuals for glmm_pql
http://imgur.com/Bg6qpnR shows qqnorm for residuals for glmm_pql
http://imgur.com/kDta9j9 shows qqplot based on random variates as above

nbquant<-rnbinom(n=length(data$outcome), size=0.97, mu=mean(data$outcome))
qqplot(nbquant,resid(glmm_pql))

My main questions now are:

1.) Can someone explain to me the differences in residual distributions?
2.) How much impact should I give the no convergence
3.) What are some general guidelines for diagnosing residual plots in 
glmers (this is a more abstract and larger question).

Thanks!
Philipp