Often, the antenna of a wireless router can be moved in many directions. Does it make a difference as to which way it points? Should it point toward the device(s) using it? Should multiple antennas (antennae?) be pointed in the same direction or different for the best connection/bandwidth?
Short version: Yes, those are probably omnidirectional dipoles. You want to orient their sides to the 2D plane where you want the most coverage.
Long version: First, beware that no antenna radiates energy equally in all directions in a 3D sphere. That would be an unattainable idealized antenna called an "isotropic" antenna.
Many antennas are "omnidirectional" which means they radiate pretty equally in all directions in a 2D disc. They don't radiate as well directly out the "ends" of the antenna. Think of a water balloon. Left alone, it's basically sphere (like an idealized isotropic antenna pattern). But if you squish it under a book on a table, you shift some of its volume from vertical to horizontal; it's less tall, but it gets wider in all directions in that 2D plane parallel to the book and table. This increase is called its "directional gain", and it is measured relative to an idealized isotropic antenna.
The most common re-orient-able antennas on consumer Wi-Fi APs are omnidirectional dipoles. They radiate well out the "sides" of the antenna, but not out of the tip-top, or the bottom (where it bends/swivels and screws into the AP). To picture its coverage pattern, imagine sliding a toy wagon wheel onto the antenna as if the antenna was an axle. Now orient the antenna so that the spokes of the wagon wheel point where you want better coverage.
If you live in a single-story home, you probably want all of the dipoles to be vertical so that the coverage pattern is horizontal. If you live in a multi-story home, I suppose you can try orienting one of them horizontally so the coverage goes "up to the second floor" or "down to the basement", but I doubt you'll find that it makes any difference.
Yes. Polarization. Waves are directional, meaning that you can affect whether a wave will pass through or be absorbed by (or partially absorbed by) a medium by changing the relative orientation of either the transmitter, the receiver, or both.
The recommended orientation of your antenna would depend on:
There's no general rules here other than experiment, but if you're one of those rare people using a beam-forming device, orientation is pretty much a solved problem, and you don't have to worry too terribly much about polarization.