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For the first part of your question: Yes, if Mallory manages to publish is own public key under Alice's name, then there is really nothing to stop him. This problem is addressed with public key infrastuctures and public key certificates. That is, for Bob to believe that the public key is Alice's key, Mallory would need to have a trusted third party attest, ...

Each additional signature halves the security level. A security level of about 64 bits can be broken by a determined attacker, and a level of 32 bits can be trivially broken on a single home computer. So if you use 256 pairs, which is a reasonable level, since it offers 256 bit security against second-preimage attacks, and 128 bits against collisions, ...

If you don't want to store the anti-CSRF tokens on the server, for most purposes it is sufficient to simply store the token as an HTTP cookie on the client. The OWASP wiki calls this technique "Double Submit Cookies". The reason this works is that, in the standard CSRF attack scenarios, the attacker cannot directly read or modify the user's cookies. ...

What do you mean by forge? If you are asking about (the common) existential forgery, then two message, signature pairs are enough, given that the messages differ in at least two bits. As an example consider that you have the signatures for $m_1 = 1111$ and $m_2 = 1100$. Considering the preimages you now have, you can forge signatures for $m_3=1101$ and ...