As for covering the face in the state of Ihram, there is nothing wrong with it according to the madhhab of Imam Ahmad ibn Hanbal. As for killing a living being in the state of Ihram, it depends on whether it is permissible to kill this living being or not. If it is permissible to kill this living being, in case one faced a snake for example, then there is nothing wrong with that. But if it is not permissible to kill this living being (pigeon or a domestic animal for example) in the state of Ihram, then the killer shall pay its forfeit in the equivalent of that which he has killed, (the forfeit) should be brought as an offering to the Ka’bah; or, he has to make an expiation by feeding poor persons, or the equivalent of that in fasting according to the judgment of two reliable and just Muslims. Almighty Allah says, “O ye who believe! Kill no wild game while ye are on the pilgrimage. Whoso of you killeth it of set purpose he shall pay its forfeit in the equivalent of that which he hath killed, of domestic animals, the judge to be two men among you known for justice; (the forfeit) to be brought as an offering to the Ka’bah; or, for expiation, he shall feed poor persons, or the equivalent thereof in fasting, that he may taste the evil consequences of his deed. Allah forgiveth whatever (of this kind) may have happened in the past, but whoso relapseth, Allah will take retribution from him. Allah is Mighty, Able to Requite (the wrong).” (Al-Ma’idah: 95)