Defining security against known-plaintext attacks does make sense in PKE. As it happens, any scheme that is secure against an eavesdropper is automatically secure against known plaintext attack as well as chosen plaintext attack. Nevertheless, it does make sense to define these classes of attacks and then show formally that security for an eavesdropper implies security against known and chosen plaintext attacks.
In fact, in Katz-Lindell they first define eavesdropper security for PKE. Then, they define CPA security, and then they show that the two are the same in the public key setting.
As you alluded to, in the public key setting, there is no difference between security from an eavesdropper and CPA-security. The reason is that an encryption oracle does not add any power to the attacker in the public key setting since the attacker has the public key and can encrypt without the oracle.
In sum then, yes it does exist, and in Katz-Lindell, they define CPA-security with PKE by giving an IND-CPA experiment in which the attacker is given an encryption oracle. But this oracle does not add any power to the attacker as an attacker can encrypt any message without the oracle. So in PKE, eavesdropper-security implies CPA-security which certainly implies security agaainst known plaintext attacks.
In regards to your last question, ditto to Dennis--there are many attacks and they vary, so listing them all is not really feasible.