First, a caveat - I'm primarily a CE, so this is just my understanding of the matter:
1. Generally, the worst reception is when the antenna is upside-down, or nearly so, and the best is when it is vertical. However, horizontal orientations are nearly as good as vertical; the radiation pattern is usually something like this, with "up" in the picture corresponding to the positive Z axis (defects overemphasized):
2. Again, your antenna manufacturer will likely have a reference design for this. Sarantel publishes sample gerbers for many of its antennas. If the antenna is not directly coupled with a ground plane, near-field radiation will still be helpful.
3. No idea. I doubt that it would matter as long as both antennas had decent signal strength. Back-to-back might not be ideal, but everywhere else should work fine.
4. No, it's hardly directional at all.The reason you use a helical antenna is because you want near-omnidirectional performance. If orientation is controllable, use a different antenna.
Yes. The 802.11 Medium Access Control, which is in charge of deciding on the data rate between two WiFi devices (which use IEEE 802.11), scales the data rate between the devices depending on a lot of things. One of them is signal strength. This correlation isn't necessarily linear, but it can be. Some packets are transmitted at 1Mbps while data is typically at the max speed. When the signal is not stable, it's common for the data rate to vary quickly. For more information see 802.11 Wireless Networks: The Definitive Guide, Second Edition
Best Answer
Yes, it does, in general.
Considering a simple half-wave dipole, which is what you're probably thinking of as an omnidirectional antenna, its radiation (or reception) pattern is strongest perpendicular to the elements, and has nulls off both ends. Additionally, the polarisation of the signal is along the elements. Since a dipole is typically mounted vertically (so it is omnidirectional with respect to the horizon), it will transmit (or receive most efficiently) vertically polarised signals.
A loop antenna can be mounted horizontally to give a horizon-omnidirectional pattern with horizontal polarisation. This will have nulls perpendicular to its plane.
A pair of cross-mounted loop antennas with a phase-shift network can be used to give circular polarisation in two specific (opposite) directions, and linear polarisation in other directions. Some people use these for contacting satellites without the need for pointing equipment.
Antenna theory is a very broad field. You should definitely choose an antenna type and mounting position to properly suit your application.