Ques 1: The 1st article says use a mechanical filter before a sand
filter. That is exactly what I am planning. There is a plastic basket
that has fairly small 1/8" slots that all the water from the drains and
skimmer go through before my sand filter. This is easily cleaned.

The basket is probably going to need to be cleaned too often to work.
I like a sloping screen where the clean water falls thru and the crud stays
on top and gradually collects at the bottom of the screen.
Look here http://www.nahuelco.com/eng/productos_tamices.php?id=1


Ques 2: Why not a sand filter w/backwash?

A swimming pool has very clean water compared to a pond.
A sand filter will need frequent cleaning/backwashing.

BTW, I am converting a
swimming pool into a pond w/ swimming "hole". I would like to use as much
of the current plumbing and filter set-up as possible.

The skimmers should work okay. You will need need new bottom drains with 4
inch pipes.


Ques 3: I read that the veggie filter should be the last thing before
re-entering the pond?

True. However if you are going to use a sand filter place it last so that
the water going into it will be as clean as possible.
Use very coarse sand or small rocks. You will need to backwash frequently.
The lost water will need to be replaced.


Ques 4: These articles don't address what a "settlement tank" is. My
original question.


A settlement tank allows the debris time to sink to the bottom. It will do
about 50% of the work.
A good one will be circular in shape with a cone shaped bottom with drain
for easy cleaning.
The water will revolve in a circle with the clean water leaving at the top.
There are other types.
Try here http://www.aquaart.com/vortex.html