Your illustration is nice but only tells part of the story. The true precession cycle takes 11,300 years. It consists of the grand loop, which your animated drawing shows, that takes 11,300 years. The smaller loops are described by the data in the table.
In other words the precession consists of the poles inscribed tens of thousands of small circles on the edge of the huge loop it inscribed across the heavens. Then there is the spiral up and down motion through our arm of the Milky Way, but we’ll save this for another time. As an aside, all of this motion has definitive impacts on global temperatures.
Correct. The graph represents the daily precession of the earth’s axis. That’s the one to be concerned about in the case of the water sloshing about in oceans. Precession will speed up or slow down to adjust for some events, such as imbalance, rotational timing, etc. Sometimes the rate of precession can change rather abruptly. The axis may even scribe a loop within the main loop! If something like that were to happened, then yes, the oceans would get sloshed around a bit, plates would move more in some cases, and earthquakes would occur. Luckily, the earth’s axis only varies by a few inches each year. The Bible speaks of events, like the sun standing still, etc., which may indicate something like the above may have occurred in our recent history by geological time frames.