i assume you want a relational database. For relational database features none can beat postgress SQL. It’s free. You can also download and use Best Database Provider for personal use only.
Yes. There are two free Editions of Informix. The full featured, but resource limited, Developer Edition can only be used to develop and test but not for production.
The Innovator-C Edition (IE), on the other hand, while it is feature and resource-limited, can be used for any purpose, including production, except that if you want to distribute it, as embedded in some application, you need to arrange a distribution license and pay a small license fee for each distributed copy. You can buy optional support for either free Edition and if you outgrow the resource limits in IE or need features it does not support, you can purchase a license for one of the four-part Editions and upgrade in place.