Yeah, I found it to involve a LOT of experiments in the Developer Tools → Template page. It’s mainly the datetime object that gives me the most trouble.
For storing values, use input_* helpers as they are called now. You’ll probably want to look at input_number.set_value service and use template in the data field.
Yes to both. See below for first, and use entities card for second
If you are not going for super sleek UI with pictures, entities card is your best friend.
Check out schedule card? I’ve not used this myself, but might help with what you want to achieve.
There’s one built in to the app? I can’t find it… may be it’s not available for early CarWings.
Don’t worry about this, it’s off topic and HA method works well for me.