Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA?
The most important property of cryptographic PRNGs is that it's indistinguishable from true random numbers, unless you know the seed, or you have huge computational resources. Two important consequences of this requirement are:


You can't find the seed from observing the output
You can't predict more outputs from observing some of them.


An attacker who can do either of those, either has broken the cryptography used in the PRNG, or he has computational resources exceeding the security level of the PRNG. For typical security levels of at least 128 bits, nobody on earth has the required resources.