What is the difference between Eutectic and Standard solder?

The eutectic point is the lowest melting point.  It varies with chemistry, so
a eutectic solder say a lead tin, would be a solder with a chemistry that gives the lowest melting point.

What is alloying in reference to soldering?
Alloying is the chemical composition.  The differences effect melting point and other properties.

What is "wetting action" in reference to soldering?
Wetting is how the solder flows.  Good wetting will give smooth flow.  Flux cleans the oxides away and aids wetting.

What is the difference between a mechanical connection and a soldered connection?
A solder connection would be better electrically.  On a pipe or tube, it would seal better.

Why is a soldered connection preferable?
I prefer solder for electrical connections or where sealing is required.