In general, a Jew is permitted to benefit from the melacha (forbidden Shabbat labor) a non-Jew does for himself or for other non-Jews.
R Daniel Braude (Learn Shabbos, pp. 521ff) writes that
a Jew can benefit from a melacha performed by a non-Jew for himself (if there is no need for more melacha to benefit the Jew),
e.g., switching a light is fine as the non-...
The Gemara (Baba Metziah 90a) discusses this:
איבעיא להו: מהו שיאמר אדם לנכרי חסום פרתי ודוש בה, מי אמרינן: כי
אמרינן אמירה לנכרי שבות - הני מילי לענין שבת, דאיסור סקילה, אבל חסימה
דאיסור לאו - לא. או דלמא לא שנא
There is a dispute in the Rishonim how to pasken.
The Rambam (Sechirus 13.3) paskens it is forbidden.
אמר לעכו"ם חסום פרתי ודוש בה. ישב לה ...
R Doniel Schreiber answers your question here (point #6)
In the period of early Shabbat when most Jews have not yet accepted
Shabbat, one who has accepted Shabbat is permitted to ask non-Jews to
perform melakha for him even if it is not for the purpose of a mitzva.
However, once most Jews have accepted Shabbat, it is permitted only if
it is for the needs of ...
In Gittin 8b The Gemora says a person may not ask a Gentile to write on Shabbos (or do any Melacha) except for writing a contract buying land in Israel then and there for fear of losing oppurtunity - כותבין עליו אונו ואפילו בשבת בשבת ס"ד כדאמר רבא אומר לעובד כוכבים ועושה
The Mishna in Shabbos is specifically talking about asking the Gentile before Shabbos ...
The Shulchan Aruch (338:6) rules that it is forbidden.
דאמירה לעכו"ם אסור בכל איסורין כמו בשבת
However, it is important to note that the exact parameters will be different to that of Shabbos. Regarding Shabbos, there are other prohibitions often mixed together with amirah lakum, which are of a different origin and therefore would not apply by other ...
Halachic decisors prohibit ordering something which is guaranteed to be delivered on Shabbat in normal circumstances (see the last paragraph for exceptions).
R Doniel Neustadt explains the general principle (here)
Amirah l’akum, giving instructions to a non-Jew to do an action which would be forbidden for a Jew to do on Shabbos, is prohibited. It
makes no ...
The first case is having a non-Jew return a cooked dry food to an open
flame. The Be’ur Halacha (Rav Yisrael Meir Kagan of Radin, 1839-1933)
rules in siman 253 that it permissible because it constitutes a Shvut
D’Shvut, a Rabbinic prohibition on a Rabbinic prohibition. That is,
telling the non-Jew to violate Shabbat is ...
R' Auerbach OBM held that refraining using electricity per se is a minhag. However, almost all electric devices involve one or more melochos, which is why it is a minhag to refrain from electricity use, since unless you are an electrical engineer AND a rav, it is unlikely that you would be able to determine what exactly is permissible and not permissible ...
You ask for sources that can be brought to support a decision. There are a number of elements to weigh in (extracted from The sanctity of Shabbos by R Simcha Bunim Cohen on the laws of non-Jews on Shabbos, pp. 29-40)
Amira l'akum: it is prohibited to tell a non-Jew to do a melacha d'orayta (forbidden Torah prohibition) on Shabbat
Shvut d'shvut: In certain ...
Shulchan Aruch Orach Chaim 319,1 specifies how to do borer on Shabbos permissibly:
ואם בירר בידו כדי לאכול לאלתר מותר:
Only if he separates with his hands (not with a specialized instrument) for eating straight away is permitted.
In the Rema Orach Chaim 319,1 explains the meanig "straight away":
הגה: וכל מה שבורר לצורך אותה סעודה שמיסב בה מיד ...
There are 2 opinions in Shulchan Aruch Orach Chaim 325,4 whether one can benefit from the bread baked by a Gentile bakery when most of its customers are gentile* straight after Shabbos/Yom Tov.
There are those who permit since the gentile made the bread in principal for other gentiles for whom prohibition of baking is of no relevance, the bread is not ...