Verb, to pass. E.g. "When walking, pass people on the right hand side," "Please pass the salt," "I passed the old shop on the corner yesterday. Preposition & adverb past. E.g. "The post office is past the supermarket," "I walk past the church every day on my way to work." Noun, past. E.g. "In the past we had fewer cars." Adjective, past. E.g. "In past times dinosaurs walked the Earth."

All the sentences are correct. And they are are in the simple narrative past. Ran past, walked past, passed ahead are all pretty close. Ran past of course is running on foot. Walked past is not running but still on foot, but, „she passed me“ could be by any means, car, train, bus anything. I also get the feel from each sentence that you were moving and not sitting, or standing still. But, in number 2 you could be sitting. „I was sitting on the bench and she passed/walked past me.“ In passed ahead I get the feeling you were moving too, but slower.