To my knowledge "Schedule" doesn't work either in Auto mode.
According to me you can use "Schedule" only for time, not temperature.
I use the TH16 to control the pump of my floor heating. During winter season the pump starts via the TH16 as soon as it registers a higher water temperature. Apart from this I have a schedule for 5 minutes every 24 hours to prevent the pump to get stuck during summer season. This schedule, every day 03:00 AM for 5 minutes, only works in manual mode.
In my app I can choose either a temperature controlled pump in Auto mode, or a time (schedule) controlled pump in Manual mode. I would like to combine those two. In that case, during summer the pump will be switched on for 5 minutes every night, but will still be operational when it is a cold day and my heat system switches on. This is not possible I think. During summer I switch to Manual mode.
Want you want for number 1 is not possible I think. Number 2 is partially possible. You can, using your app, switch to Manual mode and start the heater. The only thing is that you don't have a limited temperature. You have to switch it off manually.
For developers it might be not that difficult I think.