[RPG] Can a monk make a bonus unarmed attack after using shocking grasp

The text you've quoted is the D&D 3.5 version of Produce Flame, not the D&D 5e version. In D&D 5e, produce flame does not grant a melee touch attack, but instead allows the caster to throw the flames as a ranged spell attack.

Even if it did involve a melee attack it would be granting a new kind of attack option, not a bonus to damage of an existing attack, and would therefore not be usable with a monk's unarmed attacks.

The "Attack" action and the "Cast a Spell" action are two completely different actions, you only get 1 action per round barring specific class features. As a result unless otherwise specified no you cannot both cast shocking grasp and attack with a weapon on the same turn. (That is kinda Eldritch Knight's shindig.)