CSPRNG made out of Block Cipher running in CTR Mode?
If CSPRNG is constructed out of AES in CTR Mode, does it satisfy 2nd characteristic? i.e Compromise of internal state will not lead to reconstruction of prior stream of random numbers?


No, assuming you mean the CSPRNG is just AES in CTR, the state is simply the key and the IV, therefore compromise will allow trivial generation of both past and future outputs.

Exposure of just the key is also as bad, as you can decrypt the output using the key (in ECB mode) to recover the IV.