Verses:

When G‑d taught Moses the Torah, He also taught him the proper pronunciation and punctuation of its words: vowels, grammar, and sentence set-up—i.e. verses (pesukim). Similarly, the authors of the respective (divinely inspired) books of Prophets and Holy Writings orally transmitted to their students the division of their books into verses.

Chapters:

The division of the Scriptures into chapters (perakim) was done by non-Jews in the thirteenth century. They did so to facilitate their bible study, to make it easier to recall the exact source for any given verse.1

Torah Readings:

Moses established the custom to publicly read from the Torah scroll every Shabbat—although the entire Torah was not necessarily completed in a yearly cycle.

The custom to complete the weekly public reading of the Torah every year (on the holiday of Simchat Torah) finds its root in Babylon of the Talmudic Era. The Torah was then divided into fifty-four sections (Parshiyot) to allow for the completion of a yearly cycle with the reading of one Parshah per week.2

(Incidentally, the word "parshah" can also refer to a grouping of words or verses in the Torah. These parshiyot – which the dividers of the Torah into chapters barely took into consideration – can be as brief as two words, or as long as an entire weekly Torah reading. These parshiyot are separated in the Torah Scroll by a blank space. There are a total of 669 such parshiyot in the Five Books of Moses.)

All the best,

Rabbi Baruch S. Davidson