Manually start a program through web API is implemented. See user manual:
https://openthings.freshdesk.com/solution/articles/5000716363-api-documents
section 12: manually start a program (it’s there since firmware 2.1.7).
Enabling/disabling a program through web API unfortunately hasn’t been implemented — apologies that it fell through the crack, but it’s on the todo list now with a high priority as it’s fairly easy to implement.