Q1: Yes - just like any regression model.

Q2: Just like general linear regression, your outcome variable does not need to be normally distributed as a univariate variable. However, LME models assume that the residuals of the model are normally distributed. So a transformation or adding weights to the model would be a way of taking care of this (and checking with diagnostic plots, of course).

Q3: plot(myModel.lme)

Q4: qqnorm(myModel.lme, ~ranef(., level=2)). This code will allow you to make QQ plots for each level of the random effects. LME models assume that not only the within-cluster residuals are normally distributed, but that each level of the random effects are as well. Vary the level from 0, 1, to 2 so that you can check the rat, task, and within-subject residuals.

Q1: Yes - just like any regression model.

Q2: Just like general linear models, your outcome variable does not need to be normally distributed as a univariate variable. However, LME models assume that the residuals of the model are normally distributed. So a transformation or adding weights to the model would be a way of taking care of this (and checking with diagnostic plots, of course).

Q3: plot(myModel.lme)

Q4: qqnorm(myModel.lme, ~ranef(., level=2)). This code will allow you to make QQ plots for each level of the random effects. LME models assume that not only the within-cluster residuals are normally distributed, but that each level of the random effects are as well. Vary the level from 0, 1, to 2 so that you can check the rat, task, and within-subject residuals.

EDIT: I should also add that while normality is assumed and that transformation likely helps reduce problems with non-normal errors/random effects, it's not clear that all problems are actually resolved or that bias isn't introduced. If your data requires a transformation, then be cautious about estimation of the random effects. Here's a paper addressing this.