Welcome to Mi Yodeya, great to have you learning with us. Really inspiring that you are willing to make this step in your life. Hatzlacha, succes!
For learning Torah:
The Talmud, regarding a gentile studying Torah says:
And Rabbi Yoḥanan says: A gentile who engages in Torah study is liable to receive the death penalty; as it is stated: “Moses commanded us a law [torah], an inheritance of the congregation of Jacob” (Deuteronomy 33:4), indicating that it is an inheritance for us, and not for them.
On this, Shimeon ben Avraham Levi, in his work Oholei Torah asks nearly the same question as you, namely: there is in the Gemara a great virtue for a Gentile that studies Torah; but it distinguishes between the study of the seven mitzvot of Noach, and the rest of the Torah. So, if a gentile studies only the halachos concering the seven mitzvos, he is considered "a High Priest", according to the Gemara.
וזה המשכו של הפסוק הקודם מגיד דבריו ליעקב חוקיו ומשפטיו לישראל וכן מובא במסכת סנהדרין דף נ"ט ע"א שגם הגוי עצמו מצווה שלא ללמוד תורה ואם לומד תורה חייב מיתה וכך מובא שם בגמרא ואמר רבי יוחנן עובד כוכבים שעוסק בתורה חייב מיתה שנאמר תורה צוה לנו משה מורשה לנו מורשה ולא להם וליחשבה גבי שבע מצות מאן דאמר מורשה מיגזל קא גזיל לה מאן דאמר מאורסה דינו כנערה המאורסה דבסקילה הרי שאיסור תלמוד תורה על הגוי כלול או באיסור גזל או באיסורי עריות בכלל איסור נערה המאורסה ושם הקשתה הגמרא מברייתא שממנה משתמע שיש מעלה גדולה לגוי שלומד תורה ותירצה הגמרא שיש להבחין בין סתם לימוד תורה שזה אסור על הגוי לבין לימוד שבע מצוות בני נח שהעכו"ם חייבין בהן ובלימודם וידיעתם יש מעלה וכך מובא שם בהמשך הגמרא מיתיבי היה רבי מאיר אומר מניין שאפילו נכרי ועוסק בתורה שהוא ככהן גדול שנאמר ויקרא י"ח ה' אשר יעשה אותם האדם וחי בהם כהנים לויים וישראלים לא נאמר אלא האדם הא למדת שאפילו נכרי ועוסק בתורה הרי הוא ככהן גדול התם בשבע מצוות דידהו
Rabbi Shimeon ben Avraham Levi cites Psalms 147:19 “He declares
his Word to Ya῾aqov, his statutes and his judgments to Yisra᾽el.”.
This is also cited by the Talmud in Sanhedrin, in 59a, where the
gentile is prohibited to study Torah, and is liable to receive the
death penalty. “Moses commanded us a law [torah], an inheritance of
the congregation of Jacob” (Deuteronomy 33:4), indicating that it is
an inheritance for us, and not for them.”
However, there seem to be a contraditction, because in the Gemara it
says “but rather: A person, indicating that all people are included.
You have therefore learned that even a gentile who engages in Torah
study is considered like a High Priest.”. This, however, refers to a
gentile that studies the Torah which deals with the seven Noachide
Laws. (losely translated, still work-in-progress.)
This means that the principle mentioned in the Gemara, that a gentile cannot learn Torah, does not apply to sections in Torah that also applies to Noahides. Therefore, there are commentators that explain that a Noahide (or a gentile) is allowed to delve into Torah, but only the sections that apply to that person. See my answer here.
On doing mitzvos, commandments
As to what mitzvos (commandments) you could, should, must :) observe, there's a detailled article available on Chabad.org. See:
Do not profane G‑d’s Oneness in any way.
Acknowledge that there is a single G‑d who cares about what we are doing and desires that we take care of His world.
Do not curse your Creator. No matter how angry you may be, do not
take it out verbally against your Creator.
Do not murder. The value of human life cannot be measured. To
destroy a single human life is to destroy the entire world—because,
for that person, the world has ceased to exist. It follows that by
sustaining a single human life, you are sustaining an entire universe.
Do not eat a limb of a still-living animal. Respect the life of all
G‑d’s creatures. As intelligent beings, we have a duty not to cause
undue pain to other creatures.
Do not steal. Whatever benefits you receive in this world, make
sure that none of them are at the unfair expense of someone else.
Harness and channel the human libido. Incest, adultery, rape and
homosexual relations are forbidden. The family unit is the foundation
of human society. Sexuality is the fountain of life and so nothing is
more holy than the sexual act. So, too, when abused, nothing can be
more debasing and destructive to the human being.
Establish courts of law and ensure justice in our world. With every
small act of justice, we are restoring harmony to our world,
synchronizing it with a supernal order. That is why we must keep the
laws established by our government for the country’s stability and
harmony.
There are also other mitzvos, not included in the "traditional seven". See this answer.
I would recommend reading Sheva Mitzvos Hashem, the "Shulchan Aruch" for Noahides by Rabbi Moshe Weiner. I would also recommend reading this article.
Regarding prayer as a gentile:
Rabbi Weiner, in his Sheva Mitzvos Hashem says, cited from here:
Therefore, a Gentile needs to serve G-d in his thought and emotions to motivate himself often to love and fear G-d. How does one serve Him? By arousing his will to focus his mind and heart, to direct his thoughts and opinions so that his actions will be in accordance with the will of the Creator, which will bring pleasure and satisfaction to Him…
The main part of this service of the heart and mind is prayer.
Therefore, one should always pray before G-d, to make requests to Him
for all of his needs, and he should thank and praise Him always
according to his ability.
