Have a look at the Home-Assistant Core Rachio Integration:
The “Quick runs” and “Starting a schedule from automation” can be achieved thru the use of Scripts. I am new to HA, but managed to have my Rachio do a Quick Run thru a script, and have a trigger to automate the Quick Run script after sun down if my Weather Station registers a 95F during the day. I can also launch the Quick Run script from a button if desired.
“Preventing to run a schedule with automation (‘hold’)” is probably possible with the use of the API thru the Core built in Rachio Integration, but I just have not looked too deep as I am just setting up HA and have multiple devices I am troubleshooting. I know there is Rain Delay and Standby features available, I have never accessed them though.
I am only a week into my HA adventure, so my implementation is probably not the best, but I have achieved 2 out of the 3 asks. The above linked Documentation is not great, and I find just tinkering with the UI is more useful.
One very important note: While my automations work, I found that status is not updating and the switches will immediately turn off (even though the automation runs and status is correctly displayed in the Rachio App.). The reason is that I do not have my HA open to the Internet and use a VPN to access my HA instance. I failed to read the following note in the HA Rachio Integration Documentation…
“NOTE: In order for Rachio switches and sensors to update, your Home Assistant instance must be accessible from the internet, either via Home Assistant Cloud or another method. See the Remote Access documentation for more information.”
Also, look at the information about using an “Iframe” as that would be a very quick solution to integrate the Rachio App into a Dashboard, though it is obviously not using the HA framework really.
I plan on installing the Nginx Proxy Manager to remedy my “internet exposed HA” issue, but for now I am just happy to be able to have the HA automation running, and can still view and control everything in the Rachio App until I get more familiar with the API. I am sure the Rachio API can do all being asked for and more… I wonder if it can add more time to my days to research all this fun stuff?
I hope that is useful.