is it safe enough to do it with the above exponent (of 2^16+1), and are there any known vulnerabilities for scheme EMSA-PSS (RFC8017) or for scheme RSAES-PKCS1-v1_5 done with this signature system?
Let's go through the potential vulnerabilities:
Attack on the modulus using a conventional computer using known algorithms. In this case, the most efficient ...
Almost certainly, at least once.
It is a mistake to think of the NSA merely as a SIGINT (signals intelligence) operation. They also do defense, especially at the Information Assurance Directorate (IAD), as seen on this link to the NSA:
IAD has developed partnerships with government, industry, and academia
in order to commercialize Information Assurance (IA)...
On the Practical Exploitability of Dual EC in TLS Implementations by
Stephen Checkoway et al. (Usenix 2014) is some research that has been done on how much this NSA backdoor has affected the internet.
In short: It's hard to say. What saved a lot of systems from being compriomised is the fact that Dual_EC_DRBG was poorly executed and recommended against early....