i went back to the swamp cooler room. to your question no.1:
i power up the arduino and set the thermostat on during this condition the room temp is 25,6, so i set the hyst. to 26,5 and consequently the settemp is 28cel. i put the finger on the temp sensor ann warm it up. as soon as the room temp is one tenth higher as hyst ( that was 26,6cel), the swamp cooler comes already on, and as soon as the room drops below 26,5 the thermostat comes right off.
also something strange goes on: during this procedure, when i take my finger of the temp sensor to let it cool down it suddenly drops down to 24,4cel, and then it bounces after about 1 sec. back up to 26,6 (above hys), the swamp cooler comes on and goes right away off again, because the temp bounces back down to 24,4. this happens 2/3 times until the room temp bouncing gets smaller and smaller and levels out at the inital room temp which now about 26,1
your question no2: to get to your described state i leave the thermostat on, right now room is still 26,1 and hyst is 26,5 and settemp is 28. so to hit your desired state from question 2 i need to set the set temp at 26. before i hit 26 i push the down button only once, so when i am at settemp 27 then the swamp cooler keeps toggeling as described, on/off without and end.
another strange thing happens in the meantime: the room temp bounces again, between 23,7 and 25,9 celcius, i dont touch the sensor at all.
to get finally to your desired state from question 2 i need to push the down button again, its hesitant to do take the input. after i actually got the set temp to 25 (room temp is meanwhile 25,6) , i now need to cool down the temp sensor. i did cool the sensor below hyst temp, which is 23,5. the swamp cooler goes off. my airconditioner goes off, the temp sensor goes above hyst. and swamp cooler comes on. third time the strange behavior kicks in: the room temp. bounces from 22,8 to 25,1 cel, that makes the swamp cooler toggeling nonstop. no idea why,
now i turn the swamp cooler off: its hesitant to take this command. once its off the thermostat stays on (out of sync with the code), now the room temp is stable at 25,2 cel. i turn the thermostat button, the room temp bounces again between 22,9 and 25,2. the swamp cooler toggles...