If you look closely at the swordbearer decloaks just as they are approaching Crota. Thus, Crota was able to spot them and kill them with his sword.
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But he swung at crota which is why he decloaked
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Crota was not damaged enough by rockets. Crota must be kneeling to take damage from the swordbearer and to keep the swordbearer from being killed by Crota.
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Looked over it again and I find it worried because it takes 3 gally shots to take him down on hard and I shot 2 and there was at least 1 more so he should have went down but my friend said it was lag that causes all the glitches
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It very well could be lag. It's happen to my fire teams plenty of times.