Should I do invariance test after my CFA model was created and model fits were good? Should I do common methods bias, too? If so, how do you do these procedures in AMOS?
As far as I know, measurement invariance testing is usually performed in SEM context, when research sample contains multiple groups. In SEM context, measurement invariance is often referred to as factorial invariance. It is definitely a good idea to perform both measurement invariance analysis as well as common method bias analysis prior to creating structural models and this approach is actually recommended in the literature (i.e., Podsakoff, MacKenzie, Lee & Podsakoff, 2003; van de Schoot, Lugtig & Hox, 2012).
Gaskin (2012) provides excellent textual and video tutorials on performing CFA, including measurement model invariance testing and common method bias testing. While I don't have experience in performing CFA in AMOS (I prefer R), you are in luck :-), since many Gaskin's tutorials (and CFA ones, in particular) are focused on using AMOS. I highly recommend his materials, both textual and, especially, video. I hope that my answer is helpful.
Gaskin, J. (2012). Confirmatory factor analysis. Gaskination's StatWiki. Retrieved from http://statwiki.kolobkreations.com
Podsakoff, P. M., MacKenzie, S. B., Lee, J. Y., & Podsakoff, N. P. (2003). Common method biases in behavioral research: A critical review of the literature and recommended remedies. Journal of Applied Psychology, 88(5), p 879-903. doi:10.1037/0021-9010.88.5.879 Retrieved from http://isites.harvard.edu/fs/docs/icb.topic1392661.files/PodsakoffMacKenzieLeePodsakoff2003.pdf
van de Schoot, R., Lugtig, P., & Hox, J. (2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 1(7). doi:10.1080/17405629.2012.686740 Retrieved from http://mplus.fss.uu.nl/files/2012/07/van-de-schoot-Lugt-Hox-2012-EJDP-Measurement-invariance.pdf