I agree too. In British English "relations" and "relatives" are interchangeable.
A relative is anyone who is related to you, through marriage or through blood, such as parents, grandparents, aunts, uncles and cousins. A cousin is specifically the child of your parent's sibling (i.e. the child of your aunt or uncle is your cousin). It gets more complicated when you consider, for example, the cousin of your parents, which is a "second cousin" (I think...the rules get complex)
Basically a relative is someone related to you and a cousin is a type of relative.
A (first) cousin has a parent who is the sibling of one of your parents (the common ancestor is a grandparent to both). A second cousin has a grandparent with a sibling of a grandparent of yours(the common ancestor is a great-grandparent). A third cousin has a great-grandparent with a sibling of your great-grandparent (the common ancestor is a great-great-grandparent, and so on down the generations.
The other aspect of cousins for those into genealogy is the "removed"s. This happens when the cousins are not in the same generation, not the same number of steps from the ancestor in common (your grandfather and my GREAT-grandmother were sibling, perhaps). If my first cousin and I each have a child, those two children are second cousins (see above). But the relationship between me and my first cousin's child is "first cousin once removed": the relationship between my child and my first cousin is also first cousin once removed. If my first cousin has a grandchild, the relationship between me and that grandchild is first cousin twice removed.
Similarly, if my second cousin has a child -or grandchild - my relationship with that child would be second cousin once removed; with the grandchild second cousin twice removed. Drawing a diagram may help. You can go any number of first, second, third, fourth, fifth... and also any number of once removed, twice removed, thrice removed, four times removed...
"wohnen" is used for short-term situations.
"Ich wohne bei meinen Eltern" ...because I'm at home for the summer.
"Ich wohne in Berlin" ....because I'm only here for one semester.
"leben" is used for long-term situations and situations for which your intention is long-term.
"Ich lebe jetzt in Trier" ...because I moved here and intend to stay here for a long time.
"Wohnen" refers more to your living arrangements, like when you talk about your flat, your roommates, your rent, your furniture. And "leben" describes your entire life as in your job, your friends, your everyday routines. For example, when people want to know your new address, as in where it is you physically live, they might ask "Wo wohnst du jetzt?" When they want to know where you have made your life, they might ask "Wo lebst du jetzt?" As an answer you might tell them: "Ich lebe in Stuttgart. Ich wohne mit einer Freundin zusammen."
Nouns in the plural take a final -n when used in the dative, for example, when the object of a preposition which takes the dative (aus, ausser, bei, mit, nach, seit, von, zu...) or two-way prepositions when in a situation which calls for a dative object rather than one in the accusative. There are other uses of the dative, such as certain verbs which regularly take a dative.