Is there any new concern that Curve25519 has been backdoored by the NSA? It looks like P-256 did a long time ago, and reading the Wikipedia article doesn't give that impression, wanted to check though.
So unless djb was secretly working with the NSA and willing to risk his reputation to backdoor a highly scrutinized elliptic curve, the risk is low.
0: The value of A is (poorly) explained in passing in https://cr.yp.to/ecdh/curve25519-20060209.pdf under heading "Why this curve?", but that doesn't explain any details for someone who's not a cryptographer.
It's not a matter of trusting him, instead, it's a matter of using the algorithm that requires less trust of them all (including RSA).
The closest thing to evidence of a backdoor is circumstantial: P-256 and the others use seeds that have never been fully explained. But this alone isn't particularly unusual: DES's S-boxes were similarly chosen opaquely, and we now know that the NSA did this to strengthen DES against the not-yet-public technique of differential cryptanalysis.
All that being said, Curve25519 (and Ed25519) is just better, and you should prefer it whenever you can[1].