Can angels deviate from their entrusted mission while on earth?

Yes, that's one way for them to sin.

Job 4:18 If God places no trust in his servants,
if he charges his angels with error,
19how much more those who live in houses of clay,
whose foundations are in the dust,
who are crushed more readily than a moth!

The same idea is repeated later in Job 15

15 If God places no trust in his holy ones,
if even the heavens are not pure in his eyes,
16how much less mortals, who are vile and corrupt,
who drink up evil like water!

An angel vs angel warfare is described in Daniel 10:13

But the prince of the Persian kingdom resisted me twenty-one days. Then Michael, one of the chief princes, came to help me, because I was detained there with the king of Persia

The prince of Persia either had deviated from his initial entrusted mission or soon afterward while Michael had not.

Nevermind Mohammed, you just described every mainline denomination normalizing abortion, homosexuality, and infidelity to the words of the Bible.