Hi, here are some answers I hope will help you:
1) The reason for this should be under the same reason we do not see stars during the day, regularly. Stars and to a lesser extent, the moon do not have a high enough magnitude to overcome the brightness of the sun. When the moon is full or new, it projects the highest amount of sunlight possible to the earth, and usually does break through to where you can see it in the day time. Also, the tilt of the earth does not always equate to the angle of the moon, which further constrains the issue of seeing the moon regularly. However, in some rare cases, even, we can see other planets during the daytime. Venus and Mars are sometimes seen when they reach close proximity to the earth.
2) You should be able to detect the equidistant planet by a number of means:
- Spacecraft sent from the Earth to other planets/objects should detect another planet that is equidistant from earth
- Any radio signal should bounce off of the other planet and return to earth, as it would take time for such a signal to reach said planet and return to earth
I'm sure there are more ways to detect such a planet, but those are 2 I can think of quickly. If you study, we have already found asteroids that circle the sun behind the earth - That is, the earth has drug their orbit into a similar pattern to earth. We've detected such objects that are almost equidistant, so we should be under the assumption that if there was a planet, we would have easily seen it by now.
Back from the dead, I'm afraid.
