A spellcaster must have a hand free to access components or to hold a spellcasting focus but it can be the same hand that perform somatic components.
Yes, but in case of a paladin or cleric's shield with an emblem on it, it'd still require a free hand if the spell requires a somatic component. Even if you don't need a free hand since your spellcasting focus is drawn on your shield as an emblem. Sorcerers Apprentice took care to mention that he houserules that you need no free hand for somatic spells if you got a spellfocus on your staff. I assume it's the same with shields and emblem.
It seems unfair to me for half the spellcasting classes.