The FAIR principles guidelines aim to enhance the discovery and usage of digital objects by humans and computational agents. They are formulated at a high level and, as such, are interpreted and implemented in different ways by communities of practice. Practical approaches outlining FAIR-related characteristics of digital objects are few and far between. This paper analyzes the FAIR principles while considering distinct proposed metrics, questionnaires, and tools for manual, automated, and semi-automated FAIR assessment. Here, we present an improved questionnaire for the FAIR characterization of digital objects. Our goal is not to give a FAIRness grade for digital objects, but to outline their properties related to the FAIR principles, at any point of their data life cycle. Different communities can use the questionnaire to characterize their assets. It is designed from the outset with the additional objective of supporting the creation of bespoke metrics and assisting in automated assessment in the future. We evaluated the questionnaire by applying it to characterize data digital objects from two data repositories of materials science, the ones from Materials Cloud and PubChem.