During doing analysis in R, when I want to know 1) whether there is an effect of B and 2) whether there is an effect of C
That's OK, provided that B and C are unrelated. But if there is a causal link between them (direct or indirect) then you will need to fit a different model to assess the impact of each variable. It is also necessary to consider the causal links with all the variables. The main point here is that you have to avoid conditioning on a mediator or a collider. See here for more details:
How do DAGs help to reduce bias in causal inference?
why do I have to compare these two models (Model1 ,Model2)
Well, you have fitted two model and if you want to make some inferences about your data, then I don't see any way to avoid some kind of comparison.
And I did AIC and BIC test, if the Model 2 is better one, what is important information?
The usual criteria is that you choose the model with the lowest AIC or BIC.
And I got information of each models in console: values of Scaled residuals, Random effects, Fixed effects of each factor and their interactions and Correlation of fixed effects of each factor and their interactions Are they not important for analyzing?
The most important information is the estimates of the regression coefficients for the fixed effects (main effects and interactions). The information you listed is mostly for checking diagnostics (eg no correlations between fixed or random effects of close to +/-1), no variance component (random effects) close to zero, and perhaps an assessment of normality of the residuals.