Is there a relationship between the planetary disk and the disk of our galaxy?
No. One is from the leftovers from the formation of *one* star, the other is the set of *all* the stars in that galaxy.
What I *PRESUME* (but correct me if I'm wrong) is why would those two structures look similar at such different scales. It has to do with dynamics, and more specifically to a conservation law called "conservation of angular momentum", from which you can explain why a rotating system under a gravitational potential would form a disk. If you haven't learnt about it in high school, you will learn it if you attend the first year of a college physics undegratuate course.
Do the planetary disks for most solar systems in the galaxy form oriented in the same plane as the Galaxy itself?
No. The orientation of the planetary disk's rotation axis has to do with local effects (perturbation from neighbours) than with the whole galaxy.
In fact, you'll notice that the coordinate system known as galactic coordinate system is pretty much slanted relative to the ecliptic (the "plane" on which the Earth orbits the Sun, and around which most material in the solar system orbits the Sun). This coordinate system traces more or less along the Milky Way, which does not lie along the ecliptic.
http://en.wikipedia.org/wiki/Galactic_coordinate_systemThe Kepler Telescope depends on planets passing between between the sun it orbits and the telescope in order to be detected.
Almost that. You can make direct detections from direct measurements. This transit method allows to measure the "width" of the planet, for example.
You can still measure the presence of planets (and their distances to the star, by their periods) of exoplanets by measuring the "wobble" of the host star. That's the most common method of detection. Although if the exoplanets around a star are orbiting it perpendicularly to our line of sight, we won't measure a "wobble". This wobbling is measured more accurately in direction of the star, and not "to the sides", because you're measuring the radial Doppler shift over many days or even months.
Planets orbiting in a plane perpendicular to our view of that solar system will never be detected.
If they do, it'll have to be done in some other clever way. For example, if it's close enough and the planet is big, you might attempt a direct detection by occulting the star (putting a "dot" on the telescope that prevents light from being seen by blocking its light) and attempt to directly "see" orbiting planets. You might have some luck with large planets, but not so much with smaller planets.
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