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][1].


  [1]: http://onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2005.00391.x/abstract