As an amateur, the character is limited in what weapons can be used while on horseback to the horseman's mace, the horseman's flail and the horseman's pick, as well as the dagger and club. The character can use a scimitar (or scimitar variant), the damage from the weapon suffers a penalty of -1.
The character does not get a to hit bonus when fighting down at opponents while on horseback, because the character is considered to be challenged by the mastery of both the horse and weapon with this degree of knowledge and ability.
The character can charge on the horse and does get normal bonuses. See Charging while Mounted.
See Horseback Riding