Questions regarding the poisson model

[Nitzan04]

Hello, I'm running a poisson regression and I would like to check the goodness of fit. My dependant variable is the number of patent application per year per firm. I have several question:
Is the LR statistic is a good indication for goodness of fit ?
How do i check if i have overdispersion?
Finally, what are the most important steps i should do in order to understand how good my model is (is it searching first of all of suspicious of multicollinearity?!)