In the first article, did I commit libel? Does it matter whether or
not I had reason to believe what I published was accurate?
The short answer
You didn't commit libel, and your belief does matter. If you knew the person was innocent at the outset you might have liability.
The long answer
In U.S. Constitutional law, the minimum standard for imposing defamation liability upon a media defendant regarding a matter of public interest, such as whether a criminal at large has been caught, was articulated in the U.S. Supreme Court case New York Times Co. v. Sullivan, 376 U.S. 254 (1964), which remains good law. This requires a showing of either knowledge of falsity, or reckless disregard for the truth. This is a publisher's intent based standard.
Furthermore, a statement is generally not subject to defamation liability if the factual basis for a statement is disclosed, as it generally would be in the body of the news story, and which would generally include a press release or statement from the law enforcement agency that made the arrest. The law permits you to make an overstated headline and then pull your punches with a more balanced body text to support it, so long as you make clear that the basis of your conclusion is the facts that you disclose and you don't imply that you are relying on other undisclosed facts for your conclusion.
The statement made also needs to be interpreted reasonably and not in an unduly literal or hyper-technical manner. In this context, someone familiar with how the criminal justice system in the United States works, would know that "Rapist caught" almost surely, on its face, means that someone suspected of a rape has been arrested, and not that someone has been convicted beyond a reasonable doubt by a jury of that crime. An interpretation that you had direct knowledge that the arrested suspect was guilty would be unreasonable under the circumstances which the headline itself makes clear.
Thus, it is very unlikely that this headline would give rise to defamation liability for the reporter or the firm that published the story, unless you had knowledge that the suspect who was arrested was innocent at the outset.
U.S. defamation law is atypically globally (i.e. it is pro-speech compared to the laws of most other countries), however, and isn't a good guide to the majority rules of defamation law outside the U.S.