Haven't heard of an "Adari pool".
Look on Google Earth - follow the old road out of Manama towards Isa Town. Just past Jidhafs, on the left hand side is a grove of (trees?) and then a narrow lane terminating in a blue pool (at N26 11 57.76 E50 32 38.43) just north of the 'new' dual carriageway. Maybe it's not accessible now, but it used to be very popular with the locals for a swim at 'weekends'. Very quiet during the week, when you could see some very large fish swimming about in the very clear water. I'd guess it was a natural artesian well, which had been encased in concrete steps for access, but below the waterline you could see the sandstone sides very clearly.
The 'zoo' was the old 'Government Farm', which was on the right hand side (north side) of the Budaia road, just before the road fell away down the slipway. Looking at Google earth, it's changed out of all recognition since I was there, but I would guess the old zoo / farm was in the 'green' area just north of the large roundabout very near the end of the current dual carriageway.
Think I picked out our old house a bit north east of there though - used to be right on the beach - not any more!
Thanks for the quick nostalgia trip.
RC