Like most JDMs, the green temperature light appears on the Alto 660 dashboard when the engine is started after a few hours and will simply turn off when the engine reaches operating temperature. You will only get to see the Red temperature light if the engine overheats, normally there is no light.
To turn off eco idle feature, use the button on the dashboard on the left behind the steering wheel.
Not really needed though unless the traffic is crawling in which case it would make sense to keep the engine started.
No negative effects on the battery if it is of full amperes / OEM.