What would a moon with a six-month orbital period look like from the earth?
A moon with a sixth month period would be about 1.3 million km from Earth. That puts it close to the edge of the Earth's Hill sphere, and probably isn't stable in the long term.  So the biggest thing you might notice is &quot;goodbye moon&quot; (and having the moon in an Earth crossing orbit wouldn't be pleasant in the longer term, a collision would melt the crust)
Your questions:

One day.  The moon's motion is mostly due to the rotation of the Earth.
The moon would be very distant and small but moonrise would happen just as it does now.
Tides would be much reduced.
The cycle from new moon to full moon would take much longer. Nights at full moon would be much darker than they are now. The moon is less likely to be tidally locked, so might show different faces at different times.