Yea
An answer to can you work on the weekends yes I can do either Saturday or Sunday
Go to the Brooklyn botanic gardens
Yes, you can volunteer. They usually work as a group on Saturdays, but there are always exceptions. Just ask for Jim or Ritch, they can help you get started.
The sign on the gate of the garden states that the volunteers get together and work on the garden on Saturday. You can also contact them to verify.
To my knowledge the gardens were not developed to completion die to financial problems. This is why they are neglected. I do not think there are volunteers but you should check with the NYC Parks Department or try 311 for advice.
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