Is there a JLPT questions database from previous years exams?

The Try! series, Shin Kanzen Master, and Sou Matome are the ones most often recommended for the individual test sections (like, each one has a Vocab, Kanji, Grammar, etc book). Though not all of those resources are available for all levels.

There are also just practice tests made by a variety of companies and if you search for JLPT 模擬試験 you’ll find stuff. Those usually come with 2 or more practices tests that are the exact length of the real test, and usually a CD or links to audio downloads for the listening section.