doctor,
Horizontal full wave loop antennas are not directional if they are fairly symmetrical in shape. An odd shaped one will have some directivity, not too predictable, mostly.
Vertical full wave loops are directional, just like the driven element of a 'quad'. The shape of the loop also determines the 'shape' of the radiation pattern to some extent, sort of.
How high should one be, horizontal or vertical? As high as you can get it! More higher is more better, just like almost all antennas.
The input impedance of a typical full wave loop is something on the order of 100 - 150 ohms. Using a 1/4 wave matching section of 75 ohm coax, then 50 ohms to the radio is one common way of matching that that. Don't expect a 1:1 SWR, but do look for it to be around 1.5:1 give or take a little.
Or, feed the thing with ladder line through a tuner and who cares what the input impedance is, won't matter.
Skip or local? Both. Maybe not consistently, but as consistent as using any other kind of antenna.
You can also pick the polarity you want, horizontal of vertical polarization, depending on the shape of the thing (just like a 'quad'). A square loop fed in the middle of one side yields a horizontal polarization. Feeding it at one corner yields a vertical polarization.
A full wave loop usually has about 2 dBd gain, sort of. That depends on a lot of things, height, environment, color if the wire used, etc. Another advantage is that a loop, being a 'closed circuit' antenna, is typically quieter than a dipole or vertical. Not a lot quieter, but some.
Really want an antenna that can be used almost anywhere/band? Huge loops are very nice. If it's more than one wave length, as in two, or three, there is more gain achieved. It gets sort of directional though and may not be in the direction you want (this is with a horizontal loop, by the way, but a vertical one does about the same thing).
I like loop antennas. They tend to do as well as most others, and better in some cases. Also like to feed them using ladder line and a tuner. Tends to work fine on any band higher than what it's made for. Are they the 'end-all' of antennas? 'Course not, but they sure are handy thingys to have.
- 'Doc