Where can I find academic CV samples containing minor research projects for PhD applications without publications?
There is no need to follow a standard or template unless the specific job you apply for explicitly states that you should do so (which is rarely the case).

I am a biophysicist, not a mathematician, but from what I have seen you can put on your CV whatever you want, especially in academia: it is your CV. You should definitely include your minor research projects. You can have a look at templates for some inspiration but it is up to you how you organise your CV and which sections you include or not.

Publications usually only count if they are published in international peer-reviewed journals or books. You can possibly stretch this definition a little by including conference proceedings, abstracts, application notes, and so on, but it may be viewed as strange if you call these a "publication" (mathematicians, please correct me if this is different for you). In any case, this is the topic of your other question and is better discussed there.