Using chip antennas over a 50 foot distance

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.

The oscillator modules from Sparkfun you are linking to are not meant for RF transmission. You need a transmitter/receiver pair for each parking spot, assuming you are mimicking a system that would have distances of more than 3 feet. A Sparkfun module that you might look at is: RF Link Transmitter - 434MHz WRL-10534. In a simple minded system you could use transmitter/receiver pairs with four different frequencies. If all there spots were close to each other but far from the entrance, you could use one transmitter/receiver pair with different codes for the spots.

In the title of the question you use the phrase "power multiple LEDs". I assume you are not literally powering the LEDs, but signaling them.

For the very short distance in your model, I do not think much of an antenna would be needed.