What is the religious ruling on the Imam deputizing another person to lead the people in prayer for some of the obligatory prayers, and is it permissible for him to deduct an amount from his salary and give it as charity in exchange for these prayers?

If the absence is due to a necessary matter or a known need, and people customarily overlook it, then there is no blame upon you for being absent after appointing someone to take your place. You will not be required to have your salary deducted for these times, and if you do so, you will have the reward of charity. It is not permissible to be absent for reasons other than what has been mentioned.