Do I need a permit or like permission to have a picnic there with friends?

No, just go grab a table.

All picnicking there is free unless there's a special event going on and then they usually have signs on the street telling you about that

Call the city of elk grove

The tables are first come first claimed, with the exception of Rotary Grove and a few select pad picnic areas that require a reservati0n through Elk Grove CSD.

No

No you do not