All your problems can be solved with one thing,
Getting some game sense. The most basic thing that separates you from the blueberries running around in crucible or any game. Game sense is a mixture of actual gun skill, predictability and common sense. There are only so many places an enemy can come through in lanes/paths and they're always be patterns in everyone's gameplay. You can also predict where enemies might look to cut off in lanes and flank or outgun them. This is usually why teammates are shit in most games because they don't have basic common game or tactical sense.
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Very true. I've been working hard to learn maps, spawn points, snipe lanes etc. learning how the different classes move etc.