What constitutes a poor person? If someone is a student, and they are living off of loans without a current income, are they considered poor and could one fulfill the mitzvah of Matanos L'Evyonim by giving charity to them?
Halichos Shlomo 19:20 says a (Ani) poor person is one who does not have צרכים הכרחיים לפרנסת ביתו - basic needs for his household.
Halichos V'Hanhogos of Rabbi Elyashiv, page 24 says that one that earns a salary that does not cover all his expenses for the entire year is a עני גמור real poor person.
The status of an 'Evyon' is given to one who's financial status is less than that of an 'Oni' (Rashi, Shmos 23:6). Therefore, one should try to give Matanos LaEvyonim to the destitute, and in the words of the Mekor Chaim (סימן תרצד, ס"ג): "Be careful to send to the destitute and extreme poor called Evyonim".
However, one who gives to a simple 'Oni' fulfills his obligation (ערוך השולחן סימן תרצד, ס"ג). And who is an Oni? Whoever does not make a living (תשובות הרשב"א סי' תתעב). Nevertheless, the Nitei Gavriel (פורים, פרק סז, הערה ב) quotes in the name of the Chazon Ish and the "Rabbi's of Israel" that all who are don't earn enough to live sufficiently (for him and his household) is included in 'Evyon', and Matanos LaEvyonim may be given to them.
Shulchan Aruch, OC 694:3:
אין מדקדקין במעות פורים אלא כל מי שפושט ידו ליטול נותנים לו ובמקום שנהגו ליתן אף לעכו"ם נותנים:
We're not particular regarding money of Purim, but rather, anyone who sticks out their hand to take, we give him. In a place where the custom is to give to even non-Jews, we give them.
So, when you ask if people with certain criteria
are considered poor and could one fulfill the mitzvah of Matanos L'Evyonim by giving charity to them?
the answer is that those criteria are unnecessary as pertains to Matanos L'Evyonim.
According to Halachapedia here it records from the Piskei Teshuvos 694:2 (I will try and locate the source later) as defining an evyon as follows:
Nowadays, someone who doesn’t have a stable income that can support one’s family for normal expenses and doesn’t have property that’s not usually used and could be sold or if one has abnormal expenses such as for medical bills, or making a wedding for which one can not afford, is considered a poor person regarding this mitzvah.