a higher speed approach, say to 10 miles, would then need a more pronounced reduction in speed, which could require an earlier gear drop as that would create more drag.
In extremis yes, though it's speedbrake first to get the drag, gear's a bit of an untidy option but there if you really need to decelerate.
. A slower approach could mean a later lowering as it would then require more thrust to maintain speed due to the increased drag (= noise on the ground), which it would be preferable to keep to a minimum (safety permitting of course).
True, but it's pretty much industry standard that regardless of ATC's wishes the aircraft must be fully configured (gear locked down, landing flap achieved) at 1000 feet above airfield level. To achieve that whilst descending on a 3 degree glide requires gear lowering to start well before 1000'.