What are the rules for using commas and periods in Chinese?
I think using Chinese punctuation by following English punctuation rules is acceptable, but native Chinese readers may find it a little bit strange.

It is not necessary to use a period 。 to separate every pair of SVO sentences. When you want to put many related components/sentences together, you can just use commas ，.

When you are going to talk about another topic or another step, use a period to end the current sentence and start a new sentence.

In general, be brave in using commas.

For example:

使用中文标点符号时，简单地说，不要太过拘泥，只要将相关的句子成分放在一起，再用逗号隔开即可；对于无关的成分，采用句号隔开。

Translation: In general, be brave in using Chinese punctuation. If some blocks of a few sentences are related, use commas to connect them together. If some other blocks are not related to the former blocks you are talking about, use a period to separate these two topics.

虽然很多时候要同时表达时间、地点、人物、起因、经过、结果，句子会变得比较长，但是这些成分都是一起的，有联系的，所以仍然可以使用逗号。

Even though sometimes your sentence gets very long because you need to put when, where, who and how altogether, be brave to use commas because these components are, still, connected.

正确地使用逗号可以让句子的意思更加清晰并充满节奏感，正确地使用句号可以让段落更有层次感。

If you use commas correctly, your sentences will become clear and have rhythm. If you use periods correctly, the whole paragraph will be perfect in terms of grammatical structure.