It's not against the rules but there is no pavement. It's all sand, dirt, and mud.
Yes
You can , if it has large / rugged wheels tires
Agreed
I wouldn't bring a light weight umbrella stroller. Should be something heavy duty, probably with big wheels. Depends on how much walking you want to do with the stroller. Irvine Regional Park (1-2 miles away) has better paths for strollers.
It would need to be an off road type - some challenging areas.
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