The easy one first!
Some antennas appear to be shorted because of how the impedance matching circuit is made/works. A DC short isn't necessarily a short for AC at a particular frequency. What it amounts to is that there's a coil in there which is a short at DC, but can appear to be an 'open circuit' to AC at a particular frequency, it's frequency related. A typical ohm meter uses DC to measure resistance or open/short circuits. So, seeing a 'short' isn't all that uncommon.
Radials.
There are two kinds, above ground (dirt) and below ground (buried in dirt). Both do the same thing, act as the 'other half' of the antenna. Gives the typical vertical element something to 'work against'.
While they both do the same thing, they do that 'thing' a bit differently depending on where they are. The buried radials are sort of less efficient because they are covered in dirt (dirt sort of absorbs RF) and so more of them are needed to produce the desired results/characteristics.
Above ground radials are not affected as much by what's around them cuz what's around them doesn't 'absorb' RF as much as dirt does. Position and shape also have an effect on above ground radials. They also act as the 'other half' of the antenna that the vertical element 'works against'. So, to get the desired characteristics, there are a number of different numbers, lengths, shapes, etc, that can work. One is all that's really required. That can make the antenna into a vertical dipole, for instance. Or is sort of slanted to one side, an 'L'. Add a few more evenly spaced around that vertical element and the thing becomes omnidirectional. If they are all 'skootched' over to one side, then things sort of get directional in that direction (emphasis on 'sort of'). Split them to either side and it's then sort of bi-directional (same emphasis on sort of).
Another aspect of radials is that they can do impedance matching, something that has to be done for ALL antennas. For a typical above ground 'groundplane' type antenna, the 'angle of the dangle' of the radials can change the impedance seen by the transmitter. Flat radials typically produce an input impedance for a resonant 1/4 wave antenna close to something like 25-35 ohms of impedance. As those flat radials start to droop a little, that input impedance starts going up. A typical, average sort of droop around 45 degrees, give or take some, yields an input impedance closer to 50 ohms, kind of. If that sounds a bit indefinite, it's because it is. Lots of things can change the exact input impedance seen in a particular mounting environment. That's why all antennas usually require some 'tuning', right? And there you got radials.
There's so much paraphrasing in the above that I wish it could be sold by the pound! It isn't exact, or a very scientific explanation at all. But, it gets the idea across. Nothing is very simple without the required background information. After you consume that information, digest it for a while, beat it with hammers to make it fit somewhere, eat enough electrical 'Rolaids', it all starts to make some kind of sense. May not be 'good sense', but if it fits, and if you can make it work for you, who cares! And if you really want to know what/how this stuff works I'd suggest hit the books. Nasty thought, huh?
- 'Doc
