what time does the park open in the morning

It's always open really. If you have a boat and are on the water you can fish all night. However, if your just hanging out in the picnic area I think it's sunrise to sunset.

For hiking, it's typically sunrise to sunset. Unless you are doing something on the lake itself, I doubt anyone would even be there to check anything. There are many trails, and there are no gates on them.

Its open when I go to work at 6