Answers to the Questions:

(These are the exact messages I received, edited only for spelling/grammar)

NEW- 1) Where did the game name 'Marco Polo' come from?

From a kids point of view marco polo was an explorer and I mean this is obvious but it was just named after him because it involves water and maybe whoever made it up was in an ocean playing this game or something along these lines :)

OLD- 2) Complete the verse...

The way it went when I was in elementary school is as follows:

1st grade babies, second grade tots, 3rd grade angels, 4th grade snots, 5th grade
peaches, 6th grade plums, and all the rest are dirty old bums.
Needless to say, you only liked to say it when you were in third grade.

OLD- 3) Where did the game name 'Red Rover' come from?:

The name Red Rover came from the people in the Yukon Territories. The 2 main
colors of skin are white and "red". The red did not hang around the white
and so they made there own games. One of them is red rover come home which
is a game that the red played against the white. When the white won one
of the red the red would try to get him back.

There were two military units and they were constantly trading soldiers.
If the soldier killed an enemy they stayed in the unit that they were traded to,
and if they didn't kill an enemy they went back to the original unit.

Yes it does have something to do with the old military units there were
the special ranks, my dad was one, that is how I know.  When they
traded, because there were two military units with this name, they had to
go through initiation like football where they had the big metal tackle
dummies and you had to run and break through them except that there were
3 rows so it was a little harder, but that was basically where it came from.

Actually, the name Red Rover comes from the ancient Tasmanians.  They were
all sort of loony, and enjoyed throwing themselves at large groups of
people.  This is even how they fought their wars.  Whenever they did this,
they would shout, "Ved Voover!"  American immigration officials adapted
this name to the closest English words they could find.

I'm pretty sure that "Red Rover" is named for Red Rover clover.

Red Rover came from a red dog.

OLD-4) Why is a tie in Tic-Tac-Toe called a Cat's Game?:

I think a tie in Tic Tac Toe is a Cat's Game because Tac spelled backwards is Cat.

I believe this comes from a tie being considered a "scratch game".  Call
it a "Cat's Game" if you will.
Cats scratch.

Tic Tac Toe ties are called cats game because no matter how hard a cat tries
to win against its tale it never wins and yet has fun

I believe that it is a cat-mouse game.if not one of the two players gets
the point making it a tie game. therefore, cat gets mouse(point).

It's a game of skills the cat goes one way and the mouse goes another.  So
when it's a tie that's what it means cat's game.  A cat and mouse
chase.  When mouse gets away the cat looses.  And the mouse gets away.  A game
that goes in any direction just like a cat and mouse.

There was a tic on a tac on a cats toe.

Because cats scratch

[Here are 3 answers that are related.  It's not definitive, but it's the best so far]

The reason it is called a Cat's game is that usually when the game
ends in a tie it will make a letter "c" in the game board.

About Cat's Game in Tic Tac Toe--it is always possible to make a "C" out
of either the X's or O's when the game is a tie.  I believe that is the
reason.

I always believed it was called Cat's Tail because one players X's or O's
made a semi-circle like a cats tail curled up.