I'll preface this by saying that decks of cards exist in many different "patterns". These are design/artistic differences specific to region/country/etc, and these vary greatly from who (if anyone specific) is depicted to what they might be holding (weapons, symbols of royal authority, etc.). The association of modern face cards with historic or mythical personages is specific to the "Paris" pattern, and known as portrait officiel. This association has carried over to the "Rouen" pattern and thence to the "English" pattern (see more on this below). In this pattern the breakdown of face card to figure is as follows:

King

Spades: David (the Biblical figure)

Hearts: Charlemagne

Diamonds: Julius Caesar

Clubs: Alexander the Great

Queen

Spades: Pallas (the goddess Athena)

Hearts: Judith (Biblical figure)

Diamonds: Rachel (Biblical figure)

Clubs: Argine (an anagram of the Latin word regina, queen)

Jack

Spades: Hogier (Ogier the Dane, legendary figure who appears in French epic poetry such as the Song of Roland)

Hearts: La Hire (nickname for Étienne de Vignolles, French historical figure, prominent in the Hundred Years War)

Diamonds: Hector (Homeric figure, from the Illiad)

Clubs: Lancelot (Arthurian figure)

As to the second part of your question, the so-called "suicide king" of Hearts. This is a variation found in the "English" pattern, which in turn descended from the "Rouen" pattern. Beginning in the late 15th century playing cards were produced in the French city of Rouen for export to England. In the art on these early Rouen cards, the King of Hearts is depicted with an axe. In 1628 the import of foreign playing cards was banned by law to protect domestic card makers. Card makers in England were producing lower-quality knockoffs of the Rouen designs prior to this law, and continued to do so after it was passed. Artistic detail was lost or changed, and over time the axe of the King of Hearts found on the Rouen pattern transformed into the sword or dagger seen today. An illustration of this evolution is visible here. The final illustration from the Charles Goodall and Sons deck (late 19th century) is the one most closely associated with the modern 52-card deck. Goodall and Sons produced 3/4ths of all the playing cards made in Britain in the late 19th century (and these cards were heavily exported as well- they even produced a "colonial" line specifically for export to the Empire), so the Goodall design became one of the best known (and most copied) globally. It should be noted that despite the popular perception of "suicide" the king is actually depicted with the sword raised to strike from behind his head.

Also, I'm not a historian, just a guy who thinks this stuff is interesting, so I'll gladly cede the floor to a more qualified answerer when/if one arrives with more information.

Sources: International Playing-Card Society

World of Playing Cards "The Suicide King"

Edit: Added a link to information on Goodall and Sons, formatted some stuff.