1. Can I just remove the droplinks for the next week and if I do (i) do I need to remove the front ARB as well? - just take the drop link off
2. Would it have been jacking the front up that caused the droplink balljoint to pop, or would it have been on its way out anyway? In other words, is dropping the front back down a bit a necessity to stop the new one doing the same thing? - it may have caused it to happen but the ball joint on the drop link was knackered anyway, if you look its rusty and pitted. Would have happened soon anyway. You'll be fine with a new one.