If you only go to first order, combining loglinearized equations with nonlinear equations is possible (for higher orders, see [Can you mix log linearized equation with level equation?)). But you need to account for the fact that e.g. output in percentage deviations, y_hat, in linearized equation is a different variable than output in levels y as
y_hat=log(y)-steady_state(y);Regarding references, you might want to look at
mitpress.mit.edu/books/economic-dynamics-discrete-time
skchugh.com/teachingmanuscript.html
Fernandez-Villaverde, Jesus and Dirk Krüger (2012). “Advanced macroeconomics - a text for
undergraduates”. Tech. rep. University of Pennsylvania.
Krüger, Dirk (2007). “Quantitative macroeconomics: an introduction”. Tech. rep. University of
Pennsylvania
Regarding estimation, the standard reference is An/Schorfheide (2006), but I would not recommend doing before a thorough training.