"Latin characters" is short-hand for "characters from the Latin script", which is not the same as the Roman alphabet. Your post reads a bit muddled because you seem to be under the impression that nothing is standardised and precisely defined and one couldn't simply look up whether a characters is Latin script or not. (All the examples you showed are.)

> What does the line do?

Name is "stroke", function is the same as for other (diacritic) marks, it indicates a variant from the base form. http://enwp.org/diacritic