As said before - you are not responsible for particular details of non-mathematical history.  They are there to fill in context.  

Quick answers 1.3

The Mesopotamians were basically contemporary with the Egyptians.  Probably started earlier and went later.  Not reasonable to say the Babylonians are later.  

As we will see - the clay tablets are much smaller than the papyri.  

Why base 60?  Easily divisible by many numbers (2,3,5 as primes, 10, 12, works well with year length and month division, 20, 30, which then works well in month-length - could have arisen from combining several different systems).  

We will see extensively a distinction between pure and applied mathematics.   Applied mathematics is mathematics with context - solving practical problems for their purposes and devising the mathematics needed to do so.  Pure mathematics is solving problems from within mathematics - wondering what happens if, devising problems for their own sake.  

You all have been using positional numbers for almost all of your lives.  Different bases are groupings used for counting.  We work with groups of ten.  Once we get ten, we regroup to the next place/position.  So, the babylonians don't regroup in the next place until they get to sixty.  Just like 3 means either three or thirty or three-hundred (or three tenths) depending on its location, the Babylonian symbols are also dependent on their position for their meaning.  A positional system - no matter what - has strong advantages over a nonpositional system.  The Babylonian system only required two symbols and could represent arbitrarily large numbers - this is a major improvement over the Egyptian system.  This is not a mystery.  This number system is well understood.  

Sexagesimals are like decimals, but base sixty instead of base ten.  

The reciprocals may not be computed for student practice but as tables for reference for all.  

Typos in Suzuki:  The first sentence of section 1.3.2 "Babylon", says, "The disunity of the Sumerican city-states made them easy prey for any unified conqueror." I think Suzuki intended to write "Sumerian".

There's a typo on pg. 12 in the 3rd paragraph from the bottom (starts "Nabu-kudurri-usur...").  It's kind of funny actually - they point out the "correct" spelling of "Nebuchadnezzar" ("NebuchadRezzer") at the end of the first sentence, but spell it wrong in doing so ("Nebuchdrezzar").

Suzuki's point about the difficulty of cuneiform is that it is much easier to figure out what mathematics means - because of patterns and regularity - than it is to discern other meanings.  

The Babylonian number system *did* undergo some significant changes - one in particular, late in the culture a symbol was introduced for a place holder between non-zero places.  Zero is not, and has never been obvious (I didn't know anyone thought it was).  

The meaning of anything - mathematics or not - can be easily altered in any language by a simply misplaced or a miswritten symbol.  

Surely the Pythagoreans weren't the first to know the Pythagorean theorem (as we'll see), but they may have been the first to prove it.  Please do not make assumptions based on names of results - this is an important recurring theme.  Right angles are natural to notice and predict in triangles.  

I presume the Sumerians had some idea about the other cultures around them, but probably not a deep understanding.  

It's my guess that we hear more about the Egyptians than the Mesopotamians because the pyramids endured  (as the only 7th wonder to remain) whereas other cultures didn't have as many artifacts remain.

Water erodes - hence the Tigris & Euphrates move in the span of 4000 years (similar to the fact that Niagara falls is moving upstream).

§1.3.3 is mostly a transition.

I agree that it is notable that the legal standard held the higher classes to a higher standard - does seem the opposite today.  

Patterns and records are sufficient to predict eclipses.  

A degenerate cubic is a third-degree curve that could be expressed in lower degree.  A very simple example is x^3 - y^3 = 0.

Rivers make land fertile - but bring challenges of floods.
 
Problem 1.5 is probably solved in the mundane way you would expect.