I block using my 1 handed sword... do block perks only apply to blocking with a shield?

the ones only to the left side of the perk tree do, I believe.

Just elemental protection, deflect arrows and Shield Charge do not work with 2 Hand or single weapon. The bashes all work with 2 Hand and single weapon. And 2 Hand weapons actually bash for damage then a shield. About 50% more. A power bash with a daedric War Hammer will hit for 100 pts. A power bash with a daedric shield only hits for 40.

Only the perks that literally say "when using a shield."

This is off topic, but doesnt skooma actually give 15 points of stamina? Just looking at your profile pic.

Those that indicate shield in their description require a shield

^^nah it's 25. I think.

Nope. I dragged the stats together for a viewable pic.

actually not true. I myself thought this was the case too til i got later in the game because one of the last perks that says you can move at full speed (not sprint) while blocking with a shield, yet you can still move at full speed blocking with sword or a torch. (which btw if you have this perk coupled with the slow motion when enemy power attacks perk, you can be super freakin cheap and keep it in slow mo while you run full speed around enemies) I also havent got the last shield perk yet, so im not sure if that one requires a shield or not.