"...he likes to partake in outdoor activities, especially ones where he gets to enjoy the solitary of the wilderness." Am I using partake and solitary correctly?
You are using partake correctly. Although, I think you could find a stronger word for that particular sentence. As for solitary, you are not using it correctly. To keep the sentence you have intact you either need to say: "The solitary wilderness." Or "The solitary feel of the wilderness." I'm no expert in grammar, and I'm sure someone will come through and give you more. But those are my thoughts.
I would use 'participate' instead of partake in that context, I would also use solitude instead of solitary. he likes to participate in outdoor activities, especially ones where he gets to enjoy the solitude of the wilderness."
or just "he likes outdoor activities, especially when he's alone in the wilderness" or "He loves being alone in the wilderness"