This exposed client keys, not server keys. The client keys are at risk only in a handful of specific scenarios - e.g., if used to connect to rogue or compromised servers, or used for signing outside SSH.
This is not exploitable by simply passively watching traffic, so even for client keys, if you're certain that they were used in a constrained way, you should be fine. The difficulty is knowing that for sure, so it's still prudent to rotate.
No, only NIST P-521 client keys used with PuTTY are affected. The server host key signature is computed by the server (most likely OpenSSH) which is unaffected.
> (The problem is not with how the key was originally generated; it doesn't matter whether it came from PuTTYgen or somewhere else. What matters is whether it was ever used with PuTTY or Pageant.)