No. Deathtouch does not target anything. The only things that can target are spells, activated abilities and triggered abilities that use the stack, and the only ones that do are those that use the actual word 'target' in rules text. Deathtouch represents only a static ability and it doesn't use the word 'target'.
No it doesn't. Deathtouch on a creature just means that if that creature deals damage to another creature, be it combat or non-combat, that the creature dealt damage will be destroyed. The deathtouch ability doesn't target anything so hexproof will not save a creature dealt damage with deathtouch.
Everyone knows that good luck and good game are such insincere terms that any man who does not connect his right hook with the offender's jaw on the very utterance of such a phrase is no man I would consider as such.