Can you bike around the lake

+1 to Tony, use Google to find info nuggets like this: Biking Bicyclists and people on roller skates, roller blades and scooters are allowed on Tuesdays and Thursdays from noon until closing and on Sundays from opening until 11:00 a.m. on the paved Lakeside Trail and roads

Technically yes but nobody does. It's not really safe given the number of walkers and the number of blind curves.

Only certain hours, look on the website, they are listed