I am currently playing a Swashbuckler/Duelist type of character in Skyrim. I only use a one handed sword, carry no shield, and rely on quick reflexes to dodge enemies rather than block them. I have a few questions about armor effects.
1. I know that heavier armor more negatively effects your stamina, but does it actually affect your mobility? Do you move around more slowly when wearing heavier armor?
Yes it slows you down but there is a perk to remove this weakness.
2. Does wearing no armor at all (just regular clothing) have a benefit over light armor? Namely, does it give you maximum mobility and the lowest stamina hit?
You don't lose mobility or take a stam hit sprinting and it does provide very mage oriented benefits with robes(+magicka, +magicka regen, -spell cost). You can also take "Mage Armor" perk in Alteration to boost mage armor buffs by 3x.
3. Is there any benefit to not wearing a shield? I know in Oblivion and Morrowind, there didn't seem any benefit to NOT having a shield. I thought that was pretty lame.
Dual wielding, it's the highest DPS in the game in fact it nearly doubles the damage of 2h. The downside being that you can't block obviously, although 2x 1h swords have enough reach that you can manually dodge most attacks.
If you plan on going this route smithing and enchanting are MUSTS and I'd also very strongly recommend alchemy as well(mostly to get you the hilariously crazy smithing and enchanting potions).