Block and hand-to-hand: Yes, you can block without a weapon or shield equipped, but it won't reduce the damage you take. However, anything ELSE that happens when you block (recoil, counter-attack skill perks, etc.) will still occur.
If you can equip a shield and still use hand-to-hand, I'll be modding in several shields that just look like bracers.

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And in that vain if you don't have a offensive in your primary you don't get the "perks", but it still raises just the same but slower.
No, whether your skill is one of your Majors or not won't prevent you from getting the perks.
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Is there a point to trying to have your main skills to include a range of governing attributes?
In short, no. You'll want to USE skills with a range of governing attributes so you can get multipliers when you level up, but they don't need to be your majors.
I, personally, would drop Speechcraft and Mercantile. Having those start at lower levels and raising more slowly will probably have the smallest overall effect on your playing. I tend to rely more on combat skills, and then let my money do the talking.
