Sentence Correction

dear experts,

thanks in advance..

I am confused the usage of "comma + with" these days, and only got one link, but there is no analysis
desiring your further explanation and confirmation.

the sentences are excerpted from the following page, which mentions the sentences are from GMATPrep and OG.
https://www.beatthegmat.com/the-correct- ... 71330.html

As I know, "comma + with" is an adverbial modifier, modifies a phrase, or action of preceding clause,

Since 1986, when the Department of Labor began to allow investment officers' fees to be based on how the funds they manage perform, several corporations began paying their investment advisers a small basic fee, with a contract promising higher fees if the managers perform well.
(D) fees of investment officers to be based on the performance of the funds they manage, several corporations have begun

does "comma + with" describe the result of the action that corporation began playing or that how the funds they manage perform,
Does "comma + with" follow immediately the clause which is modified? or whatever?

From the bark of the paper birch tree the Menomini crafted a canoe about twenty feet long and two feet wide, with small ribs and rails of cedar, which could carry four persons or eight hundred pounds of baggage so light that a person could easily portage it around impeding rapids.
(E) baggage yet was so light

this one, I have two questions
1/ the place of "comma + with", does it violate the rule that modifier should be close following ?
I think that this one modifies the "canoe" (a noun) instead of "M crafted a canoe" (action of a clause) , right?
but does not follow immediately "canoe",
2/ comma + which.
comma + which generally follows the closest noun, obviously this case doesn't, will it be ambiguous if skip two phrases? it is easily to think that "comma + which" modifies cedar,

The peaks of a mountain range, acting like rocks in a streambed, produce ripples in the air flowing over them; the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, are known as "standing waves."
(C) crests and troughs that remain stationary although the air that forms them is moving rapidly, is

this one, I cannot understand the use of "comma + with", would you please clarify the modifier of "comma + with"?

Bihar is India's poorest state, with an annual per capita income of $111, lower than that of the most impoverished countries of the world.

confused, seems modifies the state (noun), but follows a clause, have no idea about the usage, need clarify.

According to some economists, Japan is in danger of plunging into a depressionthat, with double-digit unemployment, could severely strain a society that regards lifetime employment as a virtual right of citizenship.

confused, seems modifies the depression (noun), but follows a clause, have no idea about the usage, need clarify.

Sales of wines declined in the late 1980s, but they began to grow again after the 1991 report that linked moderate consumption of alcohol, and particularly of red wine, with a reduced risk of heart disease

modifies the phrase that particularly of red wine, or the clause that linked moderate consumption of alcohol.
not easy for me to judge, please clarify.

In addition to having more protein -than wheat does, the protein in rice is higher quality than that in wheat, with more of the amino acids essential to the human diet.
(B) rice has protein of higher quality than that in

I can understand "comma + with" further explains the action that rice has more protein.

The honeybee's stinger is heavily barbed and stays where it is inserted, with the result that the act of stinging causes the bee to sustain a fatal injury.

further describes the clause that honeybee's stinger is heavily barded.

Visitors to the park have often looked up into the leafy canopy and saw monkeys sleeping on the branches. whose arms and legs hang like socks on a clothesline.

(D) seen monkeys sleeping on the branches, with arms and legs hanging

this one modifies the manner of monkeys sleeping, -- modifies phrase,

During the early years of European settlement on a continent that was viewed as "wilderness" by the newcomers, Native Americans, intimately knowing the ecology of the land. were a help in the rescuing of many Pilgrims and pioneers from hardship, or even death.
(C) Native Americans, with their intimate knowledge of the ecology of the land, helped to rescue

there are one appositive phrase , one "comma + with" and one "comma + Ving"
"comma + with" describes the manner.

Orb-weaving spiders such as the argiope build webs that are essentially wheel-like, with an outer rim and a number of spokes emanating from the hub.

describes the manners

Turkey's economy has grown prodigiously over the past ten years, with an average annual increase of about eight percent-one of the highest growth rates in the world.

this one describes the clause that economy has grown

In the 1920's, the automobile industry dominated the American economy, with one out of every eight workers employed in an automobile-related job.

this one describes the clause that auto industry dominated economy

The proper use of the word with can be puzzling. Generally speaking, with can express one of three concepts:

• 1. accompanied by,
  2. having, or
  3. using

For example, when we say: John had dinner with Carlos.
We mean that John was accompanied by Carlos.

When we say: With $1,000,000 in the bank, the movie producer felt sure of himself.
We mean that the movie producer had $1,000,000 in the bank.

When we say: With the sword Excalibur, King Arthur united the land.
We mean that King Arthur used the sword Excalibur to unite the land.

As your examples show, the GMAT test does not require that the word with (or comma with) touch what it is "modifying." The with can be inserted pretty much anywhere. For example:

Bihar is India's poorest state, with an annual per capita income of $111, lower than that of the most impoverished countries of the world.

Regardless of whether we think that the , with modifies India's poorest state or Bihar, the sentence is unambiguous.

...the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, [is] known as "standing waves."

The , with merely means that the resulting flow pattern has crests and troughs that remain stationary.

Japan is in danger of plunging into a depression that, with double-digit unemployment, could severely strain a society that regards lifetime employment as a virtual right of citizenship.

This sentence merely means that the coming depression will have double-digit unemployment.

...the 1991 report that linked moderate consumption of alcohol, and particularly of red wine, with a reduced risk of heart disease.

This is an idiom: Link x with y.

Visitors to the park have...seen monkeys sleeping on the branches, with arms and legs hanging like socks...

This merely means that the monkeys have arms and legs that hang.

...Native Americans, with their intimate knowledge of the ecology of the land, helped to rescue...

This merely means that Native Americans had intimate knowledge of the ecology.

...webs that are essentially wheel-like, with an outer rim and a number of spokes emanating from the hub.

This merely means that the webs have an outer rim and a number of spokes.