Much of what you're asking will not be disclosed for obvious security reasons, so don't be surprised when call center people say they "don't know". They may actually not know, but even if they did, they'd be fired if they were to say anything. Nothing could be a touchier subject than online security for the financial institutions.
I don't know of reliable sources for the data you're asking about, and I don't know the banks or other firms would release it. For a bank to talk about its incidence rates of fraud would be unusual, because none of these institutions wants to appear "less safe" than their competitors. If there's any information out there then it's going to be pretty vague. None of these institutions wants the "bad guys" to know what their degree of success is against one bank versus any other. I hope that makes sense.
The smaller banks usually piggyback their data on the networks of the larger financial institutions, so they are as secure (as a general rule) as the larger banks' networks they're running on. Also, your transactions on your credit cards are not generally handled directly by your bank anyway, unless it's one of the big heavyweights like Chase or Bank of America. All transactions run through merchant processors, who act as intermediaries between merchants and the banks, and those guys are pretty damned good at security. I've met some of the programmers, and they're impressive to me (I've been a programmer for 35 years and can't put a finger on these guys!).
Most banks require that you must provide proof of identity when opening an account, and that ID must me the standards of the "USA Real ID Act". Here's an excerpt from the Department of Homeland Security website on what Real ID is:
Passed by Congress in 2005, the REAL ID Act enacted the 9/11 Commission’s recommendation that the Federal Government “set standards for the issuance of sources of identification, such as driver's licenses.” The Act established minimum security standards for state-issued driver’s licenses and identification cards and prohibits Federal agencies from accepting for official purposes licenses and identification cards from states that do not meet these standards. States have made considerable progress in meeting this key recommendation of the 9/11 Commission and every state has a more secure driver’s license today than before the passage of the Act.
In order for banks to qualify for FDIC protection, they must comply with the Real ID standards when opening accounts.
As with any business (especially online), the most effective way to minimize fraud is vigilant monitoring of data. Banks and other online financial entities have become very adept at pattern analysis and simply knowing where and what to look for when dealing with their customers. There are certainly sophisticated measures which are kept carefully out of the public eye for doing this, and obviously they're good at it. They have to be, right?
There's no way to completely eliminate fraud -- too much incentive exists for the "bad guys" to not constantly search for new ways to run their schemes, and the good guys will always be at the disadvantage, because there's no way to anticipate everything anyone might come up with. Just look at online viruses and malware. Your antivirus software can only deal with what it knows about, and the bad guys are always coming up with some new variant that gets past the filters until the antivirus maker learns of it and comes up with a way to deal with it.
Your question's a good one to ponder, and I wouldn't want to be the chief of internet security for a bank or online institution, because I'd lay awake at night pondering when the call's going to come that we finally ran out of luck! (grin)
I hope this was helpful.