Since the transit method of detecting exoplanets requires perfect alignment of orbits, would a Kepler-type telescope yield much more exoplanet data if sent out of our solar system even to relatively realistic interstellar distances (say, 0.1-0.5 light years)?
You wouldn't gain anything by being a few per-cent closer to exoplanets. However, you would gain - or rather lose - something by being further away from the sun:
You would be cold
Being cold doesn't sound like an advantage, but if you're using an IR/Visible light telescope it allows your mirrors and optics to become extremely accurate by removing thermal-warping related errors. The real-world WMAP satellite makes use of a shadow-shield (Giant sun-screen) to keep its optics chilled for very fine readings. Putting your telescope in the interstellar void means you can build a very large, very cool, very accurate, very sensitive telescope, meaning you might be able to directly observe exoplanets.
TL;DR: The colder you make your telescopes, the better they are. The further you are away from the sun, the colder you are. Ergo, interstellar telescope = good telescope.
Objectively it would not matter much where you place your telescope in the galaxy, as it would be closer to some planetary systems and farther from others.
However, there is a very real advantage to sending space telescopes farther away from our solar system. When you want to find planets precisely in that region of the galaxy!
This would appear common sense and simple, but think about an array of space telescopes, all mounted on rockets and each sent 10 light years away from the Earth, in all directions (that is, in 6 directions relative to Earth: up, down, north, south, east west). That way, we could get much, much detailed data about planetary systems in our galactic neighborhood.
A single space telescope, sent away from our solar system would not benefit us in detecting planets in all directions around us.
Yes but not in the way you think.
Moving the telescope slightly closer to the distant target stars would be little help. However, moving the telescope far enough (~550 AU) from the sun that it can use the sun as a gravitational lens would allow fantastic pictures to be taken. In fact, the image would be so greatly magnified (one article on the topic) that the telescope could only fit a few square kilometres or less of a target that's tens of lightyears away into its view.
Even for space telescopes, what improves resolution are mirror/lens size and image sensor resolution.
Focal lengths play an important part in magnification. Anyone whose taken astrophotography images with a camera hooked up directly to the telescope knows this.
When you start putting in eye-pieces that magnify, it has the same effect that it does for a photographer. The more material you put in front of the sensor, i.e. Lenses, the less focused your image will be at maximum magnification.
I would say that you would have to get pretty far away from the solar system for there to even be a noticeable impact.
Reflectors or refractors, the distance between the image sensor and the lens or mirrors, plus the lens or mirror's size determines magnification and sharpness (what good is magnification if it isn't sharp, the go hand-in-hand).