Later in the trilogy, other characters mention this trick. One character likens it to the Magic Eye pictures of our world, random dot autostereograms which appear to be a meaningless pattern until the viewer relaxes the eyes in such a way that a clear image is revealed. You can view many Magic Eye patterns here and practise Lyra's trick.
The Madonna is the Virgin Mary. As the mother of Jesus Christ it is reasonable that she becomes the alethiometer's symbol for motherhood as a whole.
Trollesund is described as Lapland's main port. It is fictional, but like many of the places in the world of Northern Lights it may be based on reality – in this case the Norwegian city of Tromsø (see Setting).
The name trollesund is taken from troll, a Norwegian fairytale monster, and sund, a common suffix for place names in Norway that literally means "straight".
Iorek is pronounced "YOR-ick"
This may be a reference to hydromancy, a form of scrying or divination using pools of liquid. Although traditionally it involves pools of water, ink is also used. A stone is dropped into the pool and predictions are divined from the ripples that result.
You can find an article here on different forms of scrying, as well as basic instructions for doing it yourself.