Can I take photos inside the prayer halls?

Usually, no. Look for 'No Photography' signs, which are very common inside halls containing statues. Photography of the outside grounds and gardens is generally permitted.

Bowing is a sign of respect, not necessarily religious participation. A polite, slight bow when entering the gate or before a statue is appropriate.

A Guide to Temple Etiquette in Japan

Dress modestly by covering your shoulders and knees, and always maintain a quiet, respectful demeanor. Follow the purification ritual at the entrance and observe posted signs regarding photography and footwear.

Purify at the chozuya. Before entering the main temple grounds, find the water pavilion (chozuya). Use the ladle to rinse your left hand, then your right hand, then pour water into your cupped hand to rinse your mouth. Tip the ladle vertically to rinse the handle before returning it.
Enter the prayer hall. If you enter a building, look for a shoe rack or provided plastic bags. Never wear shoes on tatami mats. When praying at the altar, toss a small coin into the offering box, bow deeply twice, clap your hands twice (if at a Shinto shrine) or keep hands pressed together in silence (if at a Buddhist temple), and bow once more.
Respect the silence. Keep your voice at a whisper. Avoid walking directly through the center of a pathway, as this is traditionally reserved for the deity. Stay to the sides of the path.

Can I take photos inside the prayer halls?: Usually, no. Look for 'No Photography' signs, which are very common inside halls containing statues. Photography of the outside grounds and gardens is generally permitted.
Do I have to bow?: Bowing is a sign of respect, not necessarily religious participation. A polite, slight bow when entering the gate or before a statue is appropriate.