Yes but phrased differently
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No.
Usually yes.
If most of them lie below the line, then that line isn't the best fit. The exact layout depends on what definition you use for "best fit", but any definition will produce a line that has roughly the same number of data points on each side of it.
A line of best-fit.
Because the "best fit" line is usually required to be a straight line, but the data points are not all on one straight line. (If they were, then the best-fit line would be a real no-brainer.)