Your "heading" is your direction. It can be as precise as a compass direction; the ship is heading north-northeast. Prepositions used to with travel are quite mysterious and indefinite. Sometimes there are local traditions, sometimes not. I might perfectly well tell my wife "I'm going to drive down to Framingham," "I'm going to drive up to Framingham," "I'm going to drive out to Framingham," "I'm going to drive in to Framingham," or "I'm going to drive over to Framingham." I can't even explain how I would choose--it would somehow depend on my mental picture of the trip, how eager I was, how laborious it seemed.... I don't know. Anyway, it is fairly natural to use the preposition "down" for a narrow passageway, with no exit, that someone are going deeper and deeper into. So her "heading," or direction, is "down a blind alley."

Heading/going to an unknown area/place, knowing there might be a trap or danger.

Heading in this context should be defined as the direction the person is moving. In this case she is heading "down an alley". This means that her direction is through an alley. So you see, it is not that she is "heading down" somewhere, just simply heading and in this case the somewhere is "down an alley", or through an alley, with other words. Without knowing the full context, I assume she is being hunted and the people hunting her cannot see her if she <heads> through this alley. I hope that I have explained it sufficiently. Just think of "heading" as the direction a person or thing is moving. For example, "I am heading to school".

Go along/down an alley firmly