What is latex enamel? I know that latex paint is water-based and enamel is varnish or lacquer plus pigment or paint. So is latex enamel considered to be water-based? Cleans up and thins with what?

Enamel refers to the final luster of the paint (and, somewhat to its hardness). Enamel is the highest gloss paint. Latex means it is water based and cleans up with soap and water. Don't thin it unless the can says it is okay; in that case you would use water.