|First of all, welcome to the forum!
Yes, the plating contains cadmium in some cases. Emerson, and many others plated the cages with it. You must be careful when you shine it.
Badges: Donald Coleman (member) reproduces many badges and motor tags and they are excellent. Or you can list on the BST column and someone might have a spare to sell you.
The blade: fully remove the setscrew, they get a good penetrating oil like Kroil, or PB Blaster. Not WD40. Then squirt into the hole and let it soak in fully. Repeat, then rotate the blade 90 degrees. Keep doing that until you've soaked the penetrant all around the shaft, then let it sit overnight. If it won't free up, repeat and let it sit overnight again. It will eventually free up. You can also heat the blade hub with a heat gun or carefully with a torch. Just get it real hot, not glowing. Lastly, sometimes a past owner got the blade on wrong and then cranked down on the setscrew, causing a burr on the rotor shaft that causes blade removal to be a bit@&. Last resort is to pull the motor apart to the point that you can grab the rotor or lock it in place then try to twist the blade, essentially unscrewing it. Just be careful not to torque on the hub, or wings or you risk bending the blade or loosening the rivets.
My guess is that the oil, combined with patience will work. It usually does.
It sounds like you have an Emerson Seabreeze. Always post pics when you have questions so we know what fan you have, and can see what your problem is. The Seabreeze was Emerson's cheaper line of fans. Still, when properly restored, they're better than anything made today.
Best of success with your restoration!