What techniques are used to establish a feeling of mystery in the first chapter of "To Kill a Mockingbird," and what point of view is it?
The point of view is Scout's but looking back on events, rather than living through them. This leads to one of the main techniques for introducing a sense of mystery, which was foreshadowing. Scout drops in mention of things yet to come.
There are some other techniques. Mentioning Dill's entrance into their life so specifically cues readers that this is important; a minor mystery of why is introduced. The other method for introducing mystery is to, well, introduce mystery. That is to say, Boo Radley's story is partially told. Since Scout doesn't know it all, it creates mystery.
'So just how did Jem manage to break his arm at the elbow and 'do it in' so badly that it stayed turn out and a bit shorter than the other for the rest of his life?'
The reader's curiousity about the story behind this incident is raised in the very opening paragraph to the novel. It baits the reader with a specific incident; then the story grows in plot and theme into something much bigger than a simple fracture.