Lunar matters.

[ABBAFAN]

Having nothing much to do during long weeks at sea I have been studying the phases of the moon and similar things. I was just wondering why it always seems to be the case that the period of the lunar perigee always(or at least very often) seems to coincide with the full moon. Is there a link between these or is it coincidence with just as many apogees occuring during other phases?
On another note, does the moon's declination vary with the sun's thus varying throughout the year the way the sun's passage across the sky does? I assume this wold be necessary in order for the full moon rise and set to line up with sun set and rise despite days and nights varying in lenth.

Just curious.