'50s and '60s Whites are some of my favorite designs and this one is no exception. Beautiful machine and in great shape, too.
Yes, wipe up the cam area. Grease need only be placed in the teeth between the gears; all over the cam post area doesn't do anything except make a mess.
The length knob probably needs oiling and you'll likely have to lift it up so that the underside is facing you as you sit in front of it. Following the mechanism with your eyes, oil any joints where metal meets metal or where there are screws/nuts.
Just looking at the pic of the tension assembly, it appears as though it's screwed in tight, all the way to the right. Have you loosened it all the way? What does it do? The numbers on the tension are not absolute measurements; rather, they're just relative depending upon the tension of the knob itself, so '0' on your machine wouldn't necessarily match '0' on another.
Again, great find. I'd love to have such a machine in my collection.