It is permitted to take the money on Motzei Shabbat, even if one the Jewish students themselves bring it.
One thing to point out is that it is permitted to invite a Non- Jew to the seudot Shabbat however it is forbidden to invite them for Seudat Yom Tov . As the Shulchan Aruch (OH 512 ) say: It is forbidden to cook for Non-Jews and the ore I is forbidden to invite them since you may add more food to the pot. If they just show up you don’t have to kick them out.
In regards to using the money they left for you.
There are two issues to look at. 1) If they are paying for services rendered on Shabbat 2)Something which comes to you in forbidden way on Shabbat may you use it after Shabbat.
About the issue of taking wages for on Shabbat.
The Gemara in Baba Metzia 58a: One who hires a day laborer to watch the red heifer to ensure that it is not disqualified, to watch the child to ensure that he remains ritually pure from birth in order to draw the water mixed with the ashes of the heifer, or to safeguard the seeds for the barley that will be used in the omer offering, does not give him wages for Shabbat. Therefore, if the items that the day laborer was entrusted to watch were lost on Shabbat, financial responsibility for their loss on Shabbat is not incumbent upon him, since he is not a paid bailee on that day.
The Baraita continues: But if he was a laborer hired for a week, hired for a month, hired for a year, or hired for seven years, the one who hired him gives him wages for labor performed on Shabbat as well. Therefore, if the items were lost on Shabbat, financial responsibility for their loss on Shabbat is incumbent upon him.
We learn from the Gemara that one who gets paid daily or by the hour is forbidden to take wages from what he did on Shabbat. One who gets paid weekly or monthly etc. an no n e specifies his wages are or what he did on Shabbat is permitted to take wages for what he did on Shabbat included. So rules the Shulchan Aruch Orach Chaim 306:4.
The are four reasons why it is forbidden to take Shabbat wages.
Rashi (Ketubot 64) it is part of the decree not to do business on Shabbat.
Pri Asher (siman 7) understood from the Rambam (Shabbat 24:8) who writes: this permitted for someone to guard his fruit on Shabbat . However this is Cheftzicha and should be forbidden : It seems the Rambam forbids sechar Shabbat is because of Mimtzo Cheftzecha , the only spiritual things are permitted on Shabbat but not monetary issues.
The Maharshag writes that the decree is that if one gets money from dong permitted work he might come to work forbidden work as well.
The Tzafnat Paneach says the getting paid makes this thing he did into a Melacha and Melacha is forbidden on shabbat.
Taking wages for dong a mitzvah though is different. The Shulchan Aruch (Orach Chaim 306:5) writes: Some forbid taking wages for being a Chazzan on Shabbat, but some permit it.
The Mishna Berura explains that for mitzvah the Rabbis did not forbid taking wages.
The Shulchan Aruch (Orach Chaim 585:5) though says: Someone who takes money for blowing the Shofar or being the Chazzan … will not see blessing from their work.
The Magen Avraham understood for this that there is no problem to get paid to be a chazzan on Rosh Hashana, just you will not see bracha from it. So rules the Yalkut Yosef (306:15) one who gets paid money for permitted work has who to rely on. Making Shabbat meals for the students is definitely a mitzvah and to take money for it is alright.
In regards to the fact that you got it on Shabbat.
The Gemara Chullin 15a says: With regard to one who cooks on Shabbat, if he did so unwittingly, he may eat what he cooked. If he acted intentionally, he may not eat what he cooked. This is the statement of Rabbi Meir.
Rabbi Yehuda says: If he cooked the food unwittingly, he may eat it at the conclusion of Shabbat, as the Sages penalized even one who sinned unwittingly by prohibiting him from deriving immediate benefit from the dish that he cooked. If he cooked it intentionally, he may never eat from it.
Rashi explains it depends on whether the melachah was done on purpose or accidental and If so it’s even permitted on Shabbat to derive benefit. A different Rashi writes it is forbidden on Shabbat only if he did it on purpose. The Shulchan Aruch (Orach Chaim 318:1) : One who cooks on shabbat on purpose is forbidden for him on Shabbat but permitted for others after Shabbat, if he did it accidentally it Is even permitted for him on Motzei Shabbat
The Gra argues and rules like R’ Yehuda.
This is only by one who did a Melcha which is forbidden from the Torah like cooking. However leaving money is only something forbidden from the Rabbanan. The Pri Megadim says that it is forbidden from the Rabbis it has the same halacha as Torah transgressions. The Gra is of the opinion that the we go according to R’; Meir and R’ Yehuda if one did something which was forbidden from the Rabbis accidentally on Shabbat he may use it on Shabbat. Muketzeh is only forbidden from the Rabbis.
The Chaye Adam has another leniency. We are only stringent not to derive benefit from something only if something forbidden was done to the thing, like cooking. However if nothing was done to the object just is it was brought in from the outside, if it was done accidentally it is permitted even for the persons who transgressed, and even if it was done on purpose it is only forbidden until after Shabbat. The Biur Halacha rules like the Chaye Adam by Rabbinic prohibitions.
The fore if a Non- Jew gave money on Shabbat it’s definitely permitted. If a Jew did it The Yalkut Yosef rules the if is forbidden to eat from food brought to the Bet Knesset in car on Shabbat. However that might be because it is degrading for Shabbat do that but here it does not seem so degrading so it would be permitted to take the money.