The answer to some parts of your question lie mainly in basic physics, there are a number of factors that will affect how a Tsunami will travel after the initial water displacement.
For example, is the initial displacement a point event (such as Tsunami caused by landslides), or an event occurring along a long line, such as the massive fault movement that caused the "Boxing Day" Tsunami of 2004.
A point event allows the water to spread out in all directions from that point, similar to ripples in a pond after a raindrop or pebble falls in, the energy is dissipated equally in all directions and therefore the water displacement - and thus the height of the breaking Tsunami wave - decreases rapidly.
Conversely, a linear event such as the "Boxing Day" tsunami doesn't allow the energy to dissipate equally in all directions, because at any given point along the wave-front, there is more "wave" to the 'left' and 'right' that prevent that dissipation. This allows the energy to be transferred over much greater distances, and allowing the water displacement to be preserved.
As for why some land gets passed by, this is usually an effect of the local topography, going back to the Boxing Day Tsunami example, the Maldives were less effected than they could have been because there was no continental shelf for the waves to encounter and build up on. Bangladesh and other countries north of the fault-line also suffered less than they could have done because the northern and southern ends of the fault acted like point-events, and the waves to the north and south dissipated much more rapidly than those to the east and west.