What is the expiation for someone who swore not to enter a social media site, but then entered it? And is it permissible to take money from one's mother to feed the needy for the expiation of an oath, or should one fast?

You are required to offer expiation for breaking an oath, as Allah Almighty says: "Its expiation is the feeding of ten poor people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever finds not [the means to do so] - then a fast of three days [is required]. That is the expiation for oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful" (Al-Ma'idah: 89). Since you do not possess the means to offer expiation, you may expiate by fasting. There is no harm in taking money from your mother to expiate, but she is not obligated to provide it.