Is it permissible for a pilgrim to give a general expiatory charity sufficient to cover any mistakes he may make during his state of ihram, and what is its amount, and does it require a specific intention coupled with the intention for Hajj?

The offering (hady) is not obligatory for a pilgrim or an 'Umrah (definition) performer who has not committed a prohibition that necessitates a blood offering (dam), nor neglected an obligation, nor is performing Qiran (definition) or Tamattu'. Rather, it is commendable for them to sacrifice an offering in Mecca. This recommended offering is not sufficient to compensate for errors that necessitate an offering, because what is not obligatory cannot substitute for what is obligatory. The fundamental principle is freedom from obligation unless something is committed that necessitates the offering.