Day Trips

Hello everyone :)

In the beginning of this year I posted my intinerary for my 22-days trip to Japan with my brother next March/April. Thank yo a lot again for your help. All hotels and the flight booked :)

Now I have some further questions:

1. We would like to do a day trip from Tokyo to Nikko. Is the following possible?
   Arrive 10.21 in Nikko, take bus to Lake Chuzenji and arrive there around 11.15. Kegon Waterfall and Lake Chuzenji + Lunch, Return to Nikko around 14.00 and visit Toshogu. Or should we take the train that arrives in Nikko at 9.11?

2. Day trip to Kamakura/Enoshima:
   Arrive in Kamakura around 9.30, to Hase Station and visit Daibutsu and Hasedera Temple, Lunch in Hasedera Temple/Restaurant. After that go to Enoshima and look around the Island. Is it probably possible to visit Hachimangu Shrine before Daibutsu and Hasedera?

I read also about shrine/temple manners. Do a lot tourists the purification and praying part or do they skip them?

Thank you a lot.