Calling functions like "Process DSP"?

Unfortunately not, you can’t access the process dsp button from the API. To achieve what you want I think you would need to call the render functions and bounce the sample to disk and then load into the instrument and do the tidy up stuff you describe… I think this would be possible from the API, if you need examples there is some usage of the render functions in this tool:https://forum.renoise.com/t/new-tool-3-0-render-and-slice/43102

An alternative and more difficult approach could be to code your own dsp functions like in this tool:https://forum.renoise.com/t/new-tool-3-0-offline-filter/43670