Hi.
I'll try to answer best I can:
1) Resolving is the ability of a lens to produce separate images of two close objects. It's scientific term is angular resolution and resolution is the minimum resolvable distance measured as an angle subtended at the lens.
This resolving ability is limited either by aberration (caused by imperfections on the surface smoothness and contour of the lens which bring the light to different focal points thus causing blurring) and by diffraction which is a function of the
different wavelengths of the light passing through the lens which causes slowing down and speeding up as it passes through different densities. (why prisms separate white light into colours). You can also see this effect by observing the colours formed on the surface of a CD or DVD.
So the sharpness of the image will be limited by both aberration and diffraction. If the aberration imperfection is minimised by using ultra high-quality lenses, then diffraction becomes the dominant limit as the light must always pass through the lens. But that objective lens perfection comes with a very high price tag.
2)As the objective lens diameter increases, then it's true that the image can be magnified further before running into brightness problems again. But as the lens diameter increases, then keeping the lens surface perfect becomes much harder. So the aberrations become harder to keep under control.
i.e. as the lens gets bigger, then so must it's quality to keep aberrations at bay hence to use that bigger objective diameter light gathering ability for extra magnification, the lens quality has to go up accordingly or resolution will suffer.
3) The shorter the focal length, the more powerful the lens.
But, conversely, the shorter the focal length the harder it is to keep perfect shape before those aberrations creep in.
Hence the compromise: the objective lens has a large diameter and a long focal length so not a great deal of magnification, because a large lens is easier to make if the surface curvature is not too great. It's job is to gather as much light as possible.
The light from the objective is brought to the eyepiece lens which has small diameter and short focal length because it's easier to make a small high magnification lens.
The eyepiece lens will also be composite (many lenses) to try to compensate for those omni-present aberrations.
All the light gathering is done by the large objective lens. The magnification and correction is done by the eyepiece lens.
4) See previous answers which explain.
5) It all depends on what you want to look at.
For planets the best type is a refractor of which the Keplerian is one. The objective does not need to have huge light gathering ability so magnification will be down to objective focal length and the quality of both objective and eyepiece lens'. 3" objective is a good starting point.
For deep space objects, light gathering ability of the objective lens becomes the most important factor. So a large aperture Newtonian reflector is considered the best since the magnification is not the issue (detail on stars cannot be resolved for the reasons previously given) but it's no good if you can't gather enough light to see those distant objects.
You can get a good 6 or 8" reflector for very reasonable money.
A compromise telescope is the Schmidt-Cassegrain (catadioptric) which is a compound telescope offering a much shorter tube whilst still offering the large objective diameter of the Newtonian and the benefits of of the refractor.
It's also the most expensive option for the beginner.