Antenna Directivity
The comments on antenna height above ground are generally true. Lower horizontal antennas lose their directivity and their feed-point impedance gets very low as they become "shorted out" by the earth under the dipole. Vertical antennas become slighly worse as some of their power is wasted heating the earth.
Where is True Ground
Yes. The type os soil under the antenna will allow much penetration (dry sand, rock) or very little (salt water).
Artificial Grounds
Ground radials or a counterpoise system serves as a low loss return for the antenna currents. That's why elevated radial systems are usually lower loss.
What About Ground Rods?
The purpose of ground rods is two-fold. Since they go right into the earth, they make a lightning ground for the antenna system. For that purpose, it makes sense to minimize the resistance in any connections. At 10,000 amps, even 0.01 ohm can be a lot. In this application they can be used with a radial system. The other purpose is to provide a connection to the earth to allow it to be a path for return currents to the vertical antenna. For instance, for a base-fed quarter wave vertical with 1 ampere of feed current, 1 ampere goes up the radiator. But 1 ampere comes up through the ground system too. It has to ... continuity of current, Kirchoff's Current Law, etc. That 1 ampere could come from copper, above-ground radials with fairly low losses. It could come from ground rods pounded into the earth. The currents here flow in the first few feet of soil under the antenna and onto the ground rods. The soil is usually quite resistive compared to a copper-plated ground rod, so some power is lost in the soil under the antenna. That's the reason it only makes sense to get radials out to about the distance the antenna is up. But not that much power is lost. It's only about 3 dB excess with maybe 8 radials. With 120 radials 0.4 wl each, the loss is down to 0.5 dB. For an installation at a broadcast station running 50,000 watts, you go for all you can. But if you can afford one S-unit loss, you might use just two radials and a ground rod.
What About Wire Size?
Thicker wire radiators have broader bandwidth. The minimum radiator thickness should be adequate to handle the antenna current and not have corona on the ends do to antenna voltage. Conductors in radial systems can be slightly smaller since there are usually more radials employed. For example, if #14 is deemed ok for the radiator, #20 might be ok for each of 8 radials.
Insulated or Bare Wire?
Yes, this agrees with what I have seen. Insulation on a wire seems to give it a "velocity factor" that increases with frequency, but really doesn't effect it any other way.
Coaxial-Cable Considerations
Yes. Small coax is lossier at higher frequencies. Just don't forget that 1 dB is still barely perceptible.
Contaminated Coaxial Cable
Yes, I've been burned by it. The method of using a transmitter, wattmeter, and dummy load to test it is very easy. Just read the power into a dummy load from the transmitter through the wattmeter. Say it's 100 watts. Then put the cable to be tested in-line after the transmitter and read the power into the dummy load now. Maybe it's 50 watts. So the cable is about 50% efficient and has about 3 dB loss ( L=10*log(50/100) ). Is that OK for that cable at that frequency? If so, it's OK. I have some approximate numbers on a webpage here.
Apparent SWR
I don't understand this section at all. SWR, that is Standing Wave Ratio, is the same everywhere along a uniform transmission line. If there are no "boxes" slipped into the line somewhere, we should measure the same SWR anywhere on it. The only reasons that I can think of that would produce an SWR reading that varies along the line are that the line is really part of the antenna radiator (and so is the SWR meter) or the SWR meter is not really well calibrated to that line's characteristic impedance. For instance, say we have a "nominally" 50 ohm SWR meter reading on a 50 ohm cable. If there is a 100 ohm load on the end, the SWR meter should read 2:1 anywhere along the cable (2:1 = 100/50). The SWR only depends on the ratio of the load resistance to the line's characteristic impedance. If 50 ohms is now the load, the SWR meter should read 1:1. Notice that a 100 ohm resistor is as good a power dissipator as a 50 ohm resistor or an 8 ohm resistor. Our SWR meter only tells us how close to 50 ohms the load is. This is important for power amplifiers which are often specified to make their rated power into a particular load resistance, 50 ohms commonly.
Now the impedance presented to the source does depend on the length of line connecting the load to the source. For instance, say we have a very short length of 50 coax connected to a 100 load resistor. At the input to the cable we would expect to see the 100 ohm load ... and we do. We measure a 2:1 SWR too (100/50). But say the cable is a quarter wavelength long (with a typical 0.66 velocity factor included). Now we see 25 ohms looking in. We still measure a 2:1 SWR (50/25). That's not the same load for a source to drive, but the SWR is still 2:1. Yes, it turns out that SWR could be expressed as 2:1 or 1:2 or 2 or 0.5 ... in fact, the British commonly use all SWR in the "less than 1" mode like "0.5" where in the US we say "2". Oh, well. If the line were longer at a half wave long (*0.66) we see 100 ohms again. This effect is very useful in designing matchers to get to some target impedance using transmission lines.
Now what if the SWR meter is not adjusted properly? Say the SWR meter reads no reflection for 40 ohms termination. Then it reads 1.25 with a 50 resistor as load. With a 40 ohm load it reads 1.0. But the SWR on a 50 ohm cable is 1.25. If the cable were a quarter wave long so 60 ohms would appear at the meter, the SWR meter might read 1.5 (60/40) and the SWR appears to "change as we move down the line" from 1.0 to 1.5. But we can see that it is all due to an error in adjusting the SWR meter. That shows the importance of getting the error out of the SWR meter.
The Isotropic Radiator
Just a quick comment here. An isotropic radiator is one that radiates uniformly in all directions. It has no directivity, that is, the antenna pattern is not squished out in some preferred direction like a water balloon. It's nice and spherically symmetric. Now real antennas like dipoles near real earth will probably have "gains" (in some directions) over an isotropic antenna in free space, far away from anything else. And they will probably have some "losses" in other directions. These are not "losses" like in a resistor or "gains" like in an amplifier, but just relative signal levels due to the antenna's directivity. Even a dipole in free space has 2.1 dBi (db relative to an isotropic radiator) in its preferred direction. But it has a lot of loss in dBi in the nulls off the ends. Antennas should really be compared in terms of "gain over an isotropic antenna" IN THE SAME DIRECTION OF INTEREST, OVER THE SAME SOIL, AT THE SAME FREQUENCY. For instance, one could ask how a ground mounted quarter wave vertical over sandy soil stacks up to a horizontal dipole at 30 feet "AT 10 DEGREES ELEVATION, BROADSIDE TO THE DIPOLE, AT 7 MHZ". Anything less would probably be an ill-posed question that really could not be well-answered.