My cousin, who is 7 years old, visited my home last Sunday.兩個逗點間插句,是限定或非限定用法?且代表唯一的堂/表兄弟?

理解上你有點誤解：

用兩逗號注明的"限定"或"指明"意思不是代表"唯一的堂/表兄弟"，而是化表"這個7歲的堂/表兄弟"[含意是這人可能還有其他堂/表兄弟(他們可能不是7歲)]

The adjective clause in example distinguishes the cousin from other cousins, will not be clear without it ; may be some other cousins not present at the moment of place.
eg:-My cousin who is 7 years old visited my home last Sunday(some others not present.)--a defining clause.
The adjective clause in eg only adds additional information to "the 7y.o.  because there are no other cousins.Without this adjective clause, the meaning is still complete--one cousin---Such a clause is known as a non-defining clause.
eg:-(as posting):-My cousin, who is 7 y.o, , visited my home last Sunday.---no other cousin---a non-defining clause.
other eg:-The sun, which gave out dazzling rays, was setting.----a non-defining clause

有逗點隔開的形容詞子句（修飾語）為「非限定」性質，無逗點隔開的才是「限定」。
唯一的人或物就不用限定性質的修飾語加以限定。
My cousin, who ..., visited my home last Sunday.表示我沒有其它的cousin，這是唯一的，所以不加以限定，而用了逗號在關係子句who...的前後。

同理，有逗號隔開的名詞子句是作為「非限定性質」的同位語，而無逗號隔開的是「限定性質」的同位語。