These are actually the roots of the trees, not the trees themselves. The temple was built in the 12th century and was abandoned in the 1400s. It wasn't until the 19th century that it was "discovered" by archeologists.
City square - but see the Glockenspiel! It's an enormous cuckoo-clock. Goes off at 11am (and noon and 5pm in summer). 15 minute show of life size figures and bells.
I would recommend you come to the Blue Lagoon directly from the airport if your flight arrives at 7,8,9 in the morning. Hotel Check-in is not until 3pm and this place will relax your mind a body from the over night flight.