Question about Telescopes , observations and explanations of the observations Though I am active on Physics, I am new to Astronomy. I am an amateur astronomer, actually even worse than amateur. I have just started it.
I have a 60 mm objective 700mm focal length refractor which I mainly use with a 20 mm eyepiece.

I have a couple of questions regarding the telescope, observations and explanations behind observations. Since they are all interlinked I decided to ask them together.

1) So, firstly the basics. Regarding the resolution power of a telescope, we know from the Rayleigh criterion that diffraction does happen at the objective. But Diffraction happens when light passes through a narrow slit or bends around a corner (whose dimensions are of the order of the wavelength of light). But there is no slit and probably no bending of light. How come then do we assume a diffraction pattern to have formed when considering the derivation of the resolution of a telescope?

2) How are exit pupil and entry pupil different from the diameter of the eyepiece and objective?

3) Why on increasing the magnification does the brightness of the object reduce (the physics behind it)? I mean that if I use 4mm eyepiece then, first of all, it becomes very difficult to find the object and secondly its brightness gets reduced when compared to the brightness that I had got using a 20mm eyepiece?

4) Secondly why do the Barlow lenses reduce the brightness a lot. And why on using  Barlow lenses the field of view get smaller and the object passes twice as quickly as without the Barlow?

5) Now the biggest question. How is it possible that every time I point my telescope towards a visible planet or a star (I know it's a star because of the sky map), I see almost the same size, when stars are visible only as small dots. The stars appear to be bluish and the planets which I have seen (Mars and Jupiter) appear reddish. That's ok but a star can not be visible as a sphere. Stars appear as dots, don't they?

6)How can I make the telescope give the best results i.e which eyepiece should I use and whether I should use Barlow lenses or not?
I'll attempt to answer as many of these questions, to the best of my abilities, as I can at this late hour.

1) Lenses have an index of refraction that is different than vacuum, and air, and they are curved. ie: corners when light is concerned.

2) The entrance and exit pupils are the pupil size required to pass an "extreme" ray through an optic. Meaning that if the light ray from the optical axis was not refracted at all as it passed the optical plane, it would still pass within the pupil (entrance) and if reflected perfectly (exit). The diameters of the objective and the eyepiece are subjective, meaning that you can have, within reason, any size objective and use virtually any eyepiece. The restrictions to this would only be focal lengths. 

3) You are looking through a thicker lens and thereby reducing the light incident on your eye. Think about the shape of the lenses, look at them and it might become apparent just how much more curvature the 4mm lens has than the 20mm lens. This added curvature comes at the cost of a higher angle of incident that a light ray has to take, and thus more optic to pass through. 

4) Barlow lenses reduce the brightness a lot because you are adding additional optics. With each new addition you decrease the amount of light by a factor relative to the thickness and clarity of the optics. The Barlow lens is increasing the magnification and thereby reducing the field of view.

5) With your specific telescope (of which I have one with the exact same size/focal length) you should be able to see Jupiter as a disk, Mars too should be more than a "dot." Stars are point sources with angular diameters much too small for you to be concerned given the size of your telescope. Also, those planets appear reddish because they are-ish. Many stars will still appear colors other than blue if you can find them.

6) This is up to your discretion and desired results when observing. Please read your owners manual, or check out the telescope mfr website for recommended setups.