You are talking about Diminutive
Chinese has that, but 子 a suffix mostly has nothing to do with diminutive. In 種子, 種 already has the meaning of seed, the suffix has nothing to do with its size. It’s more of an indicator of a single noun, like 桌子 (table), 椅子(chair), 房子(house), 柱子(pole), 櫃子(cabinet), 箱子(box), 簾子(curtain), etc. The word in the front already has the full meaning, and can be used independently.
As a personal name (especially nickname), it can have a negative tone to it, like 狗子, 鬼子, 麻子, etc. I won’t translate them, but you will get the idea. It’s indicating someone is like that object. So 花子 is just someone like a flower (not always a good name though). In the past, it’s just people would use dignified words from part of the name of a gentry as a courtesy (老子, 荀子, 墨子, 孔子, 孟子).
There are cases where it is indicating as something’s offspring, like 瓜子 (Melon seeds), but used as fruit, again it might be just a suffix, like 桃子(peach), 李子(plum), or animals like 驢子(donkey), 蝦子(shrimp). Sometimes it means something of a personhood, like 男子 (man), 女子(female) becoming like adjective, 原子 is somewhat in this category, an anthropomorphism of something that is the basic unit (原 means the most fundamental, the starting point). Some in the reverse, and change adjective to noun like 量子 (quantum), A lot of the modern phrases borrowed old words with some close meanings and added the suffix to indicate some new foreign concepts without the use of loan words.
And some dialects use more suffix of 子 than other places, and like to put it in every phrases like part of the tone. That’s why I feel it could have something to do with the Old Chinese in the past evolved and merged to different regional languages (dialects in Chinese are more like different languages, even if they use the same set of written words, their pronunciations can be completely unintelligible)