The SDKs and the core, yes: draw answers from any model you prompt yourself with the prompt the core builds. The hosted API's server isn't open; it's what the paid plans pay for.
Yes, the open core: the format, the Rust core, the web, SwiftUI and Compose SDKs and the benchmark, under Apache-2.0 at github.com/morphscreen/morphscreen. The hosted API (it adds the prompt, runs the model and repairs broken lines) is the paid service, with a free plan. Issues and pull requests are welcome.