To go back to Singapore,just reverse the process from my above post,and remember the taxi pricing should remains the same. As you already got your Boarding pass when you arrive,you can straight away check in from the Departure Hall :
Same rules apply,arrive at the Departure hall an hour in advance before the departure time in your Boarding pass. Half an hour before yr departure time,Gates from Habour Bay will open and you will cross the same immigration where you 1st step into Batam.
Good luck and enjoy Batam!