Questions about moon phases/position in the sky?

It depends on how far or close you are to the equator or pole. The closer you are to the pole, the lower the moon would drift above the horizon. The closer you are to the equator, the higher the moon would drift. And a crescent ranges in several degrees. Maybe the part of the month would be easier since in just 1 day, it completes 12 degrees of it's phase cycle or 23 moon spaces across the background of stars. While the phase doesn't seem much different after 1 day. 1 day off could make the answer be off by about an hour, since 1 day out of it's 29.5 day orbit looks identical to 1/29.5 of a day off the answer, or almost an hour or about 1 moon space. And all that about the moon's appearance and it's apparent height in the sky doesn't even include it's apparent postition due to your latitude.

That would depend where exactly you lived an what time zone you were in don't you think?