I installed CTEX, and now I installed Lyx. Why?

1 and LyX are just a visual latex system. As for the so-called "China latex", it does not exist. LaTeX system only provides CJK Chinese solution, and CCT solution is basically outdated. At present, the successful scheme of Chinese support is XeTeX+XeCJK.

2. The tutorial is enough for the basic configuration of LyX, and the input is basically the same as that of word. Just look at LyX's help documentation.

3. The problem of theorem numbering is simple. It can be solved by providing the numberwithin command in amsmath macro package. This is the basic usage, which is found in many places.