It has belonged to our family for a long time.
句末有“for+一段时间”的,前面要用完成时,改后的句子“It belonged to our family for a long time.”语法是错误的.
The instrument was bought by my grandfather many years ago.
句末为“...ago.”,前面用一般过去时,改后的句子“The instrument has bought by my grandfather many years ago.”也是语法错误.
我很多年以前就买了这本书了.
I bought this book many years ago.（偏向于强调“这本书”）
如果是强调“很多年以前”,就是：
I have bought this book for many years.