Privacy means you want to be alone, you don't want other around watching or listening. "It's hard to have any privacy when you have 10 siblings."
Intimacy refers to a close connection or moment between people. It is often romantic, but it doesn't have to be. Friends can also have intimate conversations, for example, which would be conversations about topics you only have with special people or people that you trust. "They went outside to have a more intimate conversation and escape the noise of the party."
Secrecy is hiding something or keeping something confidential. "She swore him to secrecy" means she made him promise not to tell anyone.