Yes you can
The forest is only trails but Wallam lake has pick nick tables, and grills.
Yes, you may. I had a party there last weekend and, after confirming with the park officials, I brought my propane grill. According to the MA Dept of Conversation and Recreation's website: "Only a few state parks allow you to bring in charcoal grills. Most parks allow you to bring in gas grills."
To wallam lake yes although they have grills there
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