The venue has a small lot and there is plenty of street parking.
Who can say. BUT this is a public park with play structures and open grass. Feel free to bring toys, balls, coloring books, etc. Maybe not toys with projectiles. I don't know how guests feel about getting shot with water or nerf guns.
You don't have to worry about sinking into the grass. Walkways, ceremony and reception areas are paved. It is likely, however, that you will want to stroll around this lovely park. The paved walkways are rather hilly, so you may want to take that into consideration.
Yes, furry friends on leashes are welcome!
Be sure to check the weather forecast for each specific area/city you plan to visit. On any given day, weather conditions may vary greatly from one town to another. Additionally, temperatures can drop significantly in the evenings.