assumptions for panel data analysis (Random and fixed effects models)

I have a noob question concerning the estimation of a random effects model (xtreg re in stata). I hope you can help me: I have run the random effects model and accordingly a fixed effects model. Afterwords I performed a hausman test which was insignificant (confirming that my data allows to be estimated with random effects) I also confirmed this with the Breusch-Pagan Lagrange multiplier test for random effects. I am now testing the assumptions for my model, but I am unsure about all the assumptions that should be tested. For now I have tested my models for collinearity(collin), heteroscedasticity(lrtest) and autocorrelation(xtserial). I am however unsure whether I have to test for other assumptions? Maybe someone has a clue. I have some textbooks(wooldridge & Baltagli) concerning random effects modelling but since I am a econometrics-illiterate, I do not understand everything. thnx in advance!
Kind regards