Shift button is a mechanical lock to prevent you accidentally shift into R or P while moving. You dun need to press it when going from N to D or vice-versa.
The one beside the gear stick is called shift lock. It's to prevent you changing gears when the car is not switched on. You need to press it if you want to switch to N if the car cannot start. It's rarely used.
Shifting to N at traffic lights etc is a big debate. Some ppl say better as saves fuel, some say no need. Up to you really. Just don't rev the engine before you shift into D. It will wear out the the gearbox FAST. Don't press gas until you feel the gears engage. Also not good to shift from N to D while the car is moving.
Other than that auto GB relatively straightforward and Daihatsu ones rarely have any problems.