1. Resolving power and diffraction
Diffraction happens anywhere there's an edge. "It is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle." (Wikipedia) So all you need for diffraction is an obstacle of any shape - at the edge of the obstacle, the light will bend a little.
In telescopes, diffraction takes place all around the edge of the objective, be that a lens or a mirror. With a smaller objective, with a more strongly curved edge, and with opposite sides of the edge closer together, you get stronger diffraction (larger angle of deviation). With a larger objective, more straight edge, opposite sides of the edge further apart, you get less diffraction (smaller angle of deviation).
This is why larger telescopes have smaller Airy disks. It's similar to how a narrow slit makes a wider diffraction figure, whereas a wider slit makes a tighter figure. In the case of a telescope, the diffraction figure is the Airy disk - instead of having parallel diffraction zones, it's circular. A larger aperture makes a smaller Airy disk.
2. Entrance/exit pupils and apertures
For a lot of modern amateur telescopes, the entrance pupil is actually the aperture of the telescope, or the visible diameter of the objective. In some cases the instrument has an aperture stop that reduces the size of the visible part, but that's rare. In most cases diameter of mirror = entrance pupil.
The exit pupil is simply due to the way the rays of light converge after they exit the eyepiece - they converge until they're bundled in a smallest area (the exit pupil) then diverge again.
So the exit pupil is actually smaller than the diameter of the final lens in the eyepiece, because the rays keep converging for a while.
Obviously, you want to keep your eye at the eyepiece so that the exit pupil coincides with the pupil in your eye, so as to capture the greatest amount of light coming out of the scope.
EDIT: The exact place where you keep your eye does not change the size of the image. The size of the virtual image made by the telescope depends only on object size and magnification - nothing else matters. Changing the eye position only changes the amount of light that enters your visual system. (Explaining why this is would probably require a whole 'nother topic on this forum.)
3. Magnification and brightness
The amount of light captured by the scope stays the same. It is given by the size of the aperture.
But with a larger image (higher magnification) that same amount of light coming from the object is spread out over a bigger solid angle. You see the same number of photons, but now they are spread out over a larger apparent surface. Of course it will look more dim.
Same amount of butter spread over a larger slice of bread.
4. Barlow, magnification, and field of view
A Barlow increases magnification. As shown in paragraph #3 above, more magnification = reduced apparent brightness. Same thing would happen without a Barlow, but just using a much stronger eyepiece instead.
It's all about magnification. The light absorption in the glass in the Barlow is negligible.
Also, the object seems to pass more quickly through the field of view because the apparent field of view stays the same, but the whole image is magnified. Because the image is magnified, any motion within it must appear "faster". So the object will seem to pass more quickly through the same field of view.
5. Stars and planets appear the same
They shouldn't. It's a performance issue.
Stars should appear as tiny dots at low to medium magnification. They should appear as Airy disks (but still not large) at high magnification, fluctuating due to seeing (air turbulence).
Most planets (Venus, Mars, Jupiter, Saturn) should exhibit disks that are clearly bigger than the stars. Even Uranus and Neptune (which are far away) should still show disks that, upon close examination, are revealed to be bigger than Airy disks, in an instrument as small as 150 mm aperture (perhaps even smaller).
Could be a number of reasons for this. At 60 mm aperture, your scope should have enough resolving power to distinguish between the largest planetary disks (Jupiter) and any stellar Airy disks, and the rings of Saturn should start to become visible although very tiny. If that doesn't happen, then perhaps:
- It's a collimation issue. All telescopes except most refractors require periodic collimation, otherwise performance decreases
- Quality of optics. Not sure what optics you have, but if they have performance issues then the images will be bloated
As long as there are lingering issues with the instrument, higher magnification will not help.
EDIT: Stars are so far away that they are point-like objects to us. So their images in a scope "ought to be" also point-like. But they're not. This is due to diffraction and aberrations.
Diffraction I've explained above. The Airy disk is the smallest possible image of a star you could ever have in a telescope. You cannot make a stellar image smaller than that, due to diffraction.
Then there's aberrations. There are monochromatic aberrations:
- coma: the further away from the center the image is, the less point-like it becomes
- spherical mirrors or lenses DO NOT make perfect point-like images of stars. The point-like image is just an approximation. Spheres make imperfect images by their very design and shape.
- astigmatism - like coma, images near the edge of the field of view are distorted. The difference is that astigmatism makes a symmetrical distortion, whereas coma is weird shaped (like a seagull)
- field curvature - the focal plane of the primary mirror is not flat, but it's curved. So if the scope is in perfect focus in the center, it's not in perfect focus at the edge, and viceversa.
- distortion - a square grid is bloated so it looks like a curved cushion. Doesn't matter much for astronomical instruments.
Then there are chromatic aberrations, which happen with refractors because the refraction index of the objective is not the same for all color of light.
It is the hallmark of a good telescope that its aberrations are less than the size of the Airy disk, at least for most of the field of view (perhaps excluding the zone close to the edge). That instrument is said to be "diffraction limited".
If stellar images are very bloated, the instrument is likely not diffraction limited.
6. How to optimize an instrument
You could write entire books on this topic.
A Barlow is not magic. It only gives you more magnification, but magnification is the most misunderstood parameter of a scope. Unless everything else is perfect, more magnification does not help.
There's a lot of reading you could do, and there is a lot of experimentation. Here are some older topics on this stack:
How much magnification is needed to see planets of solar system?
First night on a telescope questions
Best telescope for the viewing of Nebulae, Stars and Planets
Please Guide me to buy my first Telescope