The Riddles of Epsilon by Christine Morton-Shaw

Something dark has awoken on the remote island of Lume

Jess is not pleased when her parents drag her off to live on the weird little island of Lume. But then she encounters an eerie presence in an abandoned cottage, and her anger turns to fear when it begins to lead her through a series of creepy riddles. As she slowly unravels the mysteries of Lume, she finds the writings of Sebastian, a boy who lived one hundred years ago and whose life contains unsettling reflections of her own. To her horror, the dangers he unearthed in 1894 now begin to threaten Jess and her family . . . and if Jess does not unlock the riddles in time, she may lose her mother forever.