Are righteous Gentiles / Noahides helped by Guardian Angels?

Why is the Torah’s concept of angels completely different from that of other religions, especially regarding Guardian Angels?

I don’t think that the concepts are always completely different. But the reality is described by the Torah-based tradition. In this response, I’m going to assume that you’re referring to “guardian angels” for individual people. That is different from the “guardian angels” over nations or over the Biblical founders of subsequent nations.

How does this concept change in the context of Jewish, or Noahide (righteous Gentiles), or other belief systems?

The correct approach is to understand the basic reality of the matter. This is based on Torah (i.e. the knowledge passed down for Jews and Noahides). Then you could compare it to concepts in man-made religions. But once you have the correct knowledge, there are plenty of more important and useful things to study and do.

What is the function or role of these ranking angelic beings?

G-d creates angels as the means for enclothing a limited amount of His unlimited power. They serve to accomplish certain limited actions that He wants to do in the limited spiritual and physical worlds. If G-d would reveal Himself fully in any created realm, it and the creations inhabiting it would be completely nullified. It would be like the nullification of the light of a match in the center of the sun. (In fact, it would be infinitely more nullified). Therefore, He creates the various ranks of the angels for this function. A good source to learn about this is the book True Existence. It is a translation and explanation of a Chassidic discourse by the 4th Lubavitcher Rebbe:

https://asknoah.org/books/true-existence

Do Noahides have only the Seven Laws to follow?

That is not correct. Please study the book The Divine Code, by Rabbi Moshe Weiner of Jerusalem. It is a “shulchan aruch” (codification) of the principles and details of the Torah-based Noahide Code:

https://asknoah.org/books/the-divine-code

Quoting [with explanations inserted in brackets] from Rabbi Weiner’s Introduction that is posted on our site:
https://asknoah.org/wp-content/uploads/divine-code-preface-introduction.pdf, pages 25-26,

In addition to observing the Seven Noahide Commandments with their many details [and each Noahide commandment / mitzvah has details that correspond to a number of the Jewish commandments], a Gentile is commanded to act in the proper ways that human intelligence would compel him, whether these are obligations to G-d or to other people, or to society as a whole. Even though Gentiles are not commanded in detail about these parameters of proper conduct [which are known from other of the Jewish commandments], nevertheless, G-d carefully checks and judges all the ways of every person.

There are actions for which the individual or the society is liable to be punished, since such behavior is not appropriate for the human race, even though it is beyond the scope of the Seven Commandments. Societal morality is included in the commandment of “judgments” (“dinim” in Hebrew), by which the Children of Noah were commanded to set up courts of law, and judges who will supervise and warn society about prohibited behaviors.

But G-d will look upon the ways of an individual and judge him for his every action, even if he is not under the jurisdiction of a court of law, or if the court is not able to judge him, or if the court does not know about his behavior…

Are righteous Gentiles permitted, or even obligated, to practice any of the Jewish commandments?

Quoting from Part I, Chapter 3, which is also posted on our site:
https://asknoah.org/wp-content/uploads/fundamentals-faith-chapters1-3.pdf, pages 61-63

The general rule is that any Jewish mitzvah between man and man, or between man and G-d, which has a reason and a logical benefit for a person or society, is permitted for Gentiles to perform…  However, those [Jewish commandments] that are duty-bound by logic, such as honoring one’s parents, and kindness and charity, are obligated to be kept [by a Gentile], because such is the correct way for a person to act, as befitting the image of G-d in which he was created. However, a Gentile may not keep them because it is a commandment from G-d, but rather because one is obligated to be a good, moral person.

Many prohibitions that are commanded upon Jews are obligations for Gentiles to observe based on logic, such as the prohibitions against hating others, taking revenge or bearing a grudge. A Gentile should observe these prohibitions out of human decency, and not as Divine commandments of their own. This duty is an absolute obligation upon Gentiles, and they are liable to be punished for transgressing these obligations and for acting against moral and logical practices…

How do righteous Gentiles receive guardian angels?

When a Gentile has a need of some particular nature, G-d answers that need based on his observance of his 7 Noahide commandments and their many details, and also based on his good deeds, his observance of modes of proper conduct, the good character traits he has developed, and his belief and faith in G-d. This answering of his need may be accomplished through G-d’s assignment or creation of an angel to carry out the task of bringing about the help that the person needs. But G-d has “many messengers,” and He can provide the needed help to that person by other means as well.

Also, for righteous people, G-d in His kindness will punish them for their unrepented sins during their lifetime. (This is a much lighter punishment than the spiritual punishments that are given in the afterlife). G-d reserves their reward for the spiritual afterlife of the soul. (That is a much greater reward than any reward in a physical lifetime). For “not-good” people, G-d in His righteous judgment will reward them for their good deeds during their lifetime. (This is a much smaller reward than the spiritual rewards that are given in the afterlife.) G-d reserves their punishment for the spiritual afterlife of the soul. (That is a much more severe punishment than any punishment in a physical lifetime).

Those are the principles in general. But all the details of person’s thoughts, speech and actions are observed and remembered (“recorded”) by G-d at every moment. Only G-d has the infinite wisdom by which He knows how to determine and weigh (on His “scales of judgment”) the particular merit or demerit of everything a person does. The judgment is based on the situation, spiritual standing and life-history of that particular person.

I know that all of us are to worship and believe only in G-d. That is made clear in the Noahide Laws and the Ten Sayings given to the Israelites at Mount Sinai. How can I receive information and Torah-based support on how the righteous Gentiles receive help in G-d’s eyes?

In Genesis ch. 24, G-d helped Eliezer, Abraham’s righteous servant, to find the Divinely-intended wife for Isaac. See these verses:

Gen. 24:7 – [Abraham told Eliezer,] “The L-rd, G-d of the Heavens, Who took me from my father’s house and from the land of my birth, and Who spoke about me, and Who swore to me, saying, ‘To your seed will I give this land,’ He will send His angel before you, and you shall take a wife for my son…”

Gen.24:40 – “And he [Abraham] said to me: The L-rd, before Whom I walked, will send His angel with you and make your way prosper. You shall take a wife for my son from my family…”

Gen. 24:42 – “So I came today to the fountain, and I said, ‘O L-rd, G-d of my master Abraham, if You desire to prosper my way upon which I am going.’ ”

Rashi’s explanation: “So I came today“: Today I left, and today I arrived [even though it took many days by natural means]. From here we learn that the earth shrank for him [i.e., G-d shortened his journey].

Gen. 24:48 – “And I kneeled and prostrated myself to the L-rd. I blessed the L-rd, the G-d of my master Abraham, Who led me on the true path, to take the daughter of my master’s brother for his son.”

I.e., G-d did kindness to Eliezer by revealing that he was receiving miraculous assistance.

Genesis 24:55 – And her brother and her mother said, “Let the maiden stay with us a year or ten [months]. Afterwards she will go.”

Rashi’s explanation: “And her brother and her mother said”: And where was [her father] Bethuel? He wanted to stop [Rebecca’s marriage, by poisoning Eliezer]; so an angel came and slew him. — [Genesis Rabbah 60:12]

In summary:

The essence of this topic is found in Psalm 136:4: “To Him [G-d] Who alone performs great wonders, for His kindness is everlasting.”

This means that the greatest saving miracles of all (beyond comprehension) are those done for a person by G-d alone. G-d adjusts the “natural” course of events in order to bring about a particular benefit for a particular person. The only knowledge that this help was provided – or even that the person needed that help – is with G-d alone. This point was stressed by the Baal Shem Tov, who taught that (literally) “everything happens by individual Divine Providence.”