For the last few years I've always printed the campfire permit off the Sequoia National Forest's website. It at least makes you take (and pass) a 3 or 4 question quiz about safe campfire practices before you can print out your pre-signed permit. For me it's much more convenient since I can't ever seem to get to a FS Ranger station when it's actually open. I presumed you had to "pass" some similar quiz if you picked up your permit in person.
As far as checking for campfire permits, I've had rangers ask to make sure we have one, typically when we're at the ranger station picking up our backcountry permits. In my local National Forest, there are no permits required to enter/hike the backcountry or wilderness areas but I have heard of some of the local Volunteer Wilderness Rangers (VWRs) doing campfire permit checks in the backcountry instead. For those found without, they get issued one on the spot, so there's still no repurcussions for not having one.
I don't know too many people who carry around shovels in their packs, but some National Forest Districts (like the Santa Barbara district of Los Padres NF, for example) make an effort to outfit each official backcountry campsite with a shovel or two for hikers to use for campfire duties. The FS supplies the shovels, the VWRs pack them in and leave them at the campsites. They usually last a few years before some knucklehead inevitably burns up the shovel's handle in... you guessed it! The campfire.