Would you tell me what's the best practice about following questions?

There is only good enough :) after that is all preference

1. Is cygwin necessary?

no

2. the IDE, Emacs?

I don't like IDEs :) I don't like Emacs ... I like SciTe ... http://padre.perlide.org is ok too ... I've developed with notepad too (not notepad2 or notepad++ plain old notepad) ... "the best" is something you know and are comfortable with that doesn't interfere, that helps you ... often taking the time to find out what you like best isn't worth the effort :)

3. Some mojo examples can't run in lastest stable mojo version, how can I find some example.

What examples? Try the other examples? The documentation always worked pretty good for examples for me :) my example Mojolicious::Lite +and jQuery +AJAX + Mojo::Template, Re: What does Mojolicious do exactly and is it right for me?, Re: Strange issue with Mojolicious

4. mojo + nginx is suitable in windows?

For development? No, you don't need nginx for development, you got Mojo