1. Battle of Britain wasn't failure for original plans, because in the first weeks Britain's airforce was almost completely destroyed, their airfields were almost unusable. Don't remember who said this, but some RAF general said that BoB was already lost until (Not Hermann Göring, although he was idiot too) Hitler gave the order to bomb cities not british airpower (airfield,factory,radar). This gave very important respite for RAF to fix airfields and their airpower. He did this because Churchill in some stupid/genius idea send night bombing to Berlin, which made Hitler angry and changed totally the tactics for BoB. If they had kept the original plans for BoB britains airforce would have been totally nullified and Germans would have had total air control of south&mid Britain air, like allies had in late war.
This is, or was, the conventional view that arose during the war itself, and prevailed up until about the 80's; it's the view that is expressed in the movie Battle of Britain. However, more recent work has poured cold water on the idea.
The question comes down to how important those airfields really are. And while they have there uses, they just are not critical. If the Luftwaffe had bombed every airfield to rubble, British fighters would still have been able to take off and land at improvised grass fields. Indeed, virtually the whole German effort was made from the same sort of improvised fields in France, showing how little difference they really make.
Additionally, the corner had already been turned some time before the switch to the bombing of cities. German losses were climbing way past replacement rate, while British production of aircraft and crews was constantly ramping upward. Every German pilot who bailed out over England was lost, while every British pilot who bailed out was back in the air as soon as the next day. The Germans were also fighting at the very limit of fuel capacity, which limited the time they could spend fighting, and caused losses on the return trip. (Although they did have a really excellent air-sea rescue service.)
Luftwaffe estimates of the strength of the RAF were woefully inadequate, and German crews used to caustically joke that every Spitfire they saw was the last one, as Goering had claimed. By the closing stages of the Battle of Britain, it was more a turkey shoot than a battle. Nevertheless, German efforts were increased just at the very end, to maintain strategic surprise over the Russians; but this inflicted yet more avoidable losses.
The prevailing view these days is that the Luftwaffe never came close to winning the BoB, regardless of what target they were bombing, and almost certainly never could have won it under any circumstances right from the start.