Yes, but remember this is a wildlife research area. Do not interfere with ongoing activity in the woods. Report any issues to dnr. Make sure to dress for ticks and high visibility (hunting season). Very little to be found on the trails.
Yes as previously noted you would have to go off trail as it's a pretty busy area and will be pretty well picked. Wear heavy clothes as there is lots of wild rose with pickers to navigate through.
If you have proper navigation equipment you can veer of the trail, and find morel mushrooms. however you have to be careful not to get lost, and there is a fare amount of poison ivy. Other than that, rose lake is one of my favorite places to go, and I highly recommend it
Yes you can hunt mushrooms if you can find them.
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