Brent being alive to be rescued isn't as contrived as it is at first glance—the spider likely wanted her offspring to have fresh food upon hatching.
Alex predicts that the spider will find somewhere isolated to lay her eggs, only to be proven wrong when the spider goes for city hall. He probably didn't account for the fact that this spider is big enough to be anything but stealthy and is strong enough that anything that attacks her is dinner anyway; it would actually make more sense for her to park her nest close to her food source, than try to travel so far away to avoid detection that she risks a lack of food.
How do they kill the Big-Ass Spider? By shooting her in her big ass!
