I wouldn't use CitiBike for Central Park - there's a $4 fee per each 15 mins after your first 30 mins, so unless you're planning on docking every 30 mins, I'd hire from one of the companies hiring bikes especially for the park.

Yes there are restrooms in the park see park map for locations within

Yes, there is lots of things to see and do. Best if one obtains a map and plan ahead.

No its not. Anywhere you go you should be attentive and pay attention to your surroundings. But in manhatten especially you see police walking or driving almost everywhere

The Lake is in the center of Central Park, more or less street 79.

To the park itself, there are no entry fees. There are a lot of activities that can be done within the park itself that might require an entry fee but for the most part a lot of the activities hosted are free.

few

Yes. Beautiful.

There isn't one. Dogs are allowed off-leash between 6 a.m. and 9 a.m. and then 9 p.m. to 1 a.m.

There is an ice rink in Centel park. Located in the South Eastern part of the park. Generally open during the colder months and weather dependent.