Our course at college is hard. One of my friends said he doesn't pray in the mosque because he does not get time for it as he is studying hard for the course. He is doing the course to take care of his parents in the future (as in to earn money). He gave me an example of a Hadeeth where a Sahaabi (companion of Prophet, sallallaahu alayhi wa sallam) was going for Jihaad and Prophet Muhammad, sallallaahu alayhi wa sallam, asked him if his mother was alive and this Sahaabi said 'Yes'. So messenger of Allaah told him to go and serve your mother first. Is my friend doing right by not praying in the mosque (though I assume he must be praying in his room)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

What your friend is doing is not correct because it is an obligation to perform the prayers in congregation according to the most preponderant opinion of the scholars. There are many evidences for this. Allaah says (which means): {And perform the prayer (Iqaamat-as-Salat), and give Zakat, and bow down or submit yourselves with obedience to Allaah along with Ar-Raki'oon (those who bow down or submit themselves to Allaah in obedience.}[Quran 2: 43]. Allaah Has first commanded us to establish the prayers and then to bow down with those who bow down or submit themselves to Allaah in obedience, and this is subsequent to the first act of obedience. It is known that bowing down along with those who bow down or submit themselves to Allaah in obedience is in congregational prayer [and not when performing the  prayer individually]. Please refer to Fatwa: 82538 for more details.

Allaah has ordered us to perform congregational prayer even when in a state of fear during wars as He says (which means): {And when you [O Mohammad ] are among them and lead them in prayer, let a group of them stand [in prayer] with you and let them carry their arms. And when they have prostrated, let them be [in position] behind you and have the other group come forward which has not [yet] prayed and let them pray with you, taking precaution and carrying their arms…}[Quran 4:102]. So what about your friend who stays at home in peace and does not attend congregational prayer on the grounds that the studies are hard?  There is no doubt that this is not a valid excuse. Even if his parents prohibit him from attending the congregational prayer, it is an obligation on him to disobey them and pray in congregation. Indeed, the Prophet said: "There is no obedience to a creature in matters which involve disobeying the Creator." [Ahmad] Moreover, Al-Hassan Al-Basri said: 'If a mother prevents her son from praying 'Ishaa' prayer in congregation out of mercy to him, it is not permissible for him to obey her.' [Al-Bukhari]

As regards the narration that you quoted in your question, it is narrated by Mu'aawiyah Ibn Jaahimah As-Sulami . He went to the Prophet seeking permission to go for Jihaad with him for Allaah's Sake and the sake of the Hereafter. So the Prophet asked him "Is your mother still alive?" He replied "Yes". So the Prophet told him: "Go back to your mother and be kind and dutiful to her." Therefore, being kind and dutiful to the mother comes in priority over making Jihaad in the path of Allaah. This is, of course, when Jihaad is optional and not an individual obligation; the situations when Jihaad is an individual obligation are mentioned in the books of Islamic jurisprudence. However, being kind and dutiful to the mother [or to the father or to both parents] does not mean abandoning acts of worship and acts of obedience to Allaah.

Allaah knows best.