I CAN ANSWER most of your questions with certainty; however, not the big one, which was left implied. I'll get to that one anon. As to the others (bearing in mind that I'm only speaking to the Silver Age) . . . .
Were [Superman's fingerprints] like a human's?
Yes, they were. Or, at least, they were never shown to not be like a human's. Superman was shown to have left fingerprints (in the normal fashion, the way a normal man would) on two occasions: 1) in "The Land of a Million Supermen", from Action Comics # 233 (Oct., 1957); and 2) in "Lois Lane, Super-Chef", from Lois Lane # 1 (Apr., 1958).
In addition, on at least three occasions, he was fingerprinted by authorities, incumbent due to arrest or confinement:
"The Trial of Superman", Action Comics # 301 (Jun., 1963)
"The Goofy Superman", Superman # 163 (Aug., 1963)
"Superman---Guilty of Homicide", Action Comics # 358 (Jan., 1968)
The third story above even includes a panel showing the Man of Steel being fingerprinted by the police.
In none of the above five instances is any reference, either by a character or in a caption, made to Superman's fingerprints being alien or in any way unlike a normal Earth man's prints. In addition, three of the above-mentioned tales relate Superman's efforts to recover or obliterate his fingerprints in order to keep them from potentially being compared to Clark Kent's prints, which further implies that his fingerprints look like a normal human's.
Wouldn't he have to be fingerprinted as a reporter?
By the standards of life in the 1950's and '60's, not necessarily. In that era, one was fingerprinted if he entered the military or a civil service job in government security, served in an occupation where he was required to be bonded, or was arrested. It was quite possible to go through life holding a decent job, raising a family, doing all the things one does/did in a normal social life, and never be fingerprinted. (My father, for example, lived for eighty-six years and never had his fingerprints taken.)
At that time, there was no general requirement or need to fingerprint reporters, so Clark Kent would not have been fingerprinted . . . .
At least, not for reasons of employment.
In "Clark Kent in the Big House", from Action Comics # 323 (Apr., 1965), Kent is arrested and fingerprinted as part of a state-arranged hoax to nail evidence against a prison inmate. So Kent's fingerprints were on file. (Theoretically, though, his print card might been expunged after the case was successfully completed.)
Couldn't someone compare Clark's [fingerprints] to Superman's?
Yep, they sure could. As I mentioned above, it was the Man of Steel's concern in at least three stories---the ones from Action Comics # 233 and Lois Lane # 1 and Superman # 163. In addition, Superman feared his prints as Superboy (left through non-typical means) being compared to those of Clark Kent in "The Super-Mystery of Metropolis", from World's Finest Comics # 84 (Sep., 1956).
The implied Big Question is, if Superman is aware that his fingerprints can be reliably matched to those of Clark Kent and fears that, what does he do to prevent his prints as Superman from being obtained?
We knows from reading the stories I cited that he destroyed the copies of his fingerprints in all of the stories except the two in which he was arrested---Action Comics # 301 and 358. Nothing was ever shown or explicated to the contrary, so in theory, Superman's fingerprints are still on file with the Metropolis Police Department.
With no comparison prints, simply having a copy of Superman's fingerprints poses no direct threat. Only someone with a reason to believe Superman was Clark Kent, or suspected such, would be a problem, if that person had a copy of Superman's prints. Naturally, Lois Lane and Lana Lang are the first two subjects that come to mind under that qualification, but they certainly are not the only ones. Over the course of the Superman stories, several individuals came to suspect the Man of Steel and Kent of being the same man. So having Superman's prints on record does pose a threat.
And that brings us to the point which I have not been able to confirm---yet. I seem to recall something expressed about this. I believe it was in an editor's response to a fan's letter in a letter column. As I vaguely remember, I believe the editor (and I'm sure it was Mort Weisinger at the time) explained that whenever Superman touched a surface that would retain his fingerprints, he would blur his prints by vibrating his fingertips at super-speed.
Of course, my vague memory in no way validates that solution. I haven't had time lately, but in the next day or so, I'll attempt to go through all of my Superman-related comics and see if I can find that lettercol response.
As I said, it might take a couple of days before I can do that, but I didn't want to leave your post dangling that long without some sort of reply.
Hope this helps.