Are there any common rules for arguing? Like the ethic of arguing. Where can I read them?

I don't know. However me and my guy set our own rules for arguments or disagreements. 

1) No raised voices or shouting 

2) No name calling.........

3) stick to the current issue, do not bring up past grievances 

4) Agree to disagree

Tomorrow  is our 10 year together and we have argued so few times, I don't remember when we last had an argument. 

A Rulebook for Arguments, by Anthony Weston, is good.  Its perspective re ethic of arguing is:  Socratic or true dialectic--A has some perspective, constructs an argument for it, B either counter-argues or, in the Socratic method, offers leading questions with the intent to show the fallacy in A's argument/point of view.  (This is in contrast to the illogical, circular method of arguing a conclusion by assuming it in the premises (e.g., marxism as feel-good pseudo-science).)

Weston also includes a helpful list of further resources in the last two pages of the book (pp. 87-88; probably the newer edition has more pages).

If you're Muslim (or just interested in a good exposition), would also note al-Ghazali's The Incoherence of the Philosophers (main ideas); if you're a mathematician, Franceso Berto's There's Something about Godel:  The Complete Guide to the Incompleteness Theorems; if you're a philosohper, Quee Nelson's The Slightest Philosophy. 

Written arguments follow the same comma rules as all prose.

Comma Rule Number 1: A comma is necessary to separate a compound structure, two or more main clauses joined by one of the seven coordinating conjunctions: for, and, not, but or, yet, so (which spells FANBOYS).

The woman drank black coffee, and she ate a croissant.

You can conduct yourself in a pleasant manner, or you can leave.

Evan loves Suzanne, but he cannot forget Elena.

If a writer chooses to make those constructions into simple sentences, with one subject performing two verb actions, then the comma is not used:

The woman drank black coffee and ate a croissant.

You can conduct yourself in a pleasant manner or leave.

Evan loves Suzanne but cannot forget Elena.

Comma Rule Number 2: A comma is necessary to separate a [long] introductory element before a main clause. Rule 2 holds true for both simple and complex constructions:

Even though ignorant of our culture, we must always be kind to strangers.(Simple)

Since Constance is new to our company, all of us should strive to help her.

(Complex)

It’s always correct to set off any introductory element with a comma, but a more modern leaning toward fewer commas in novels has made the practice optional for shorter elements. Either is acceptable. It’s easier to put them in and allow edits to remove them than to omit them and need to insert them.

Later, you can join us for dessert.

Later you can join us for dessert.

Comma Rule Number 3: Commas separate items in a series:

James found blondes attractive, redheads adorable, and brunettes irresistible.

The final comma before the conjunction is always correct. However, the journalistic practice to omit the serial (or Oxford) comma is every author’s option:

James found blondes attractive, redheads adorable and brunettes irresistible.

Comma Rule Number 4: Interjections and forms of address are set off with commas.

Yes, I will accompany you to the ball.

No, I won’t!

You, sir, are out of line.

You may be assured, ma’am, of our concern.

Are you certain of that prognosis, Doctor?

Thank you, Mother, for all you do.

There’s a world of difference between “Let’s eat, Grandpa” and “Let’s eat Grandpa.”

Comma Rule Number 5: Words, phrases, or clauses (appositives and infinitives included) which interrupt the main clause but are not essential information must be set off with commas fore and aft.

Mrs. Ellen Bennet, my mother, is in the drawing room.

The Brooklyn Bridge, as opposed to this Lego model, is sturdy and reliable.

He was born on June 23, 1941, in Big Timber, Montana, along the Yellowstone River.

Those earrings, in my opinion, would look better hanging over formal dining tables.

Rule 5A. The final necessary use of the comma is the most difficult for many writers. It’s actually the same as rule 5, but it’s often presented in isolation because of its difficulty. As with appositives and infinitive phrases, it separates nonrestrictive clauses in a sentence. The nonrestrictive clause is not essential to the sentence. It merely adds information:

Abraham Lincoln, who was the tallest of U.S. presidents, was an imposing figure of a man.

The grizzly, a bear misunderstood by tourists, is named Ursus horribilis for good reason.

By contrast, a restrictive clause is essential to the sentence:

Animals that attack campers are removed to more remote parts of the park.

The man who shot Liberty Valance became a state senator. .