You don't need any synergy skill to create any synergy recipie technically, it just gets easier with skill levels (and most likely, a natural increased rate of HQs like normal crafting). So you won't need any skill to augment stuff, however there will be some skill caps so you can skill up on these recepies from what the twitter said:

FFXI_EN FINAL FANTASY XI
Skill: You’ll be able to take on the augmenting of gear solo and we're planning to make the required skill level rather low. (1/2) #FFXI

That was my impression.

As for removing something from the furnace another individual has produced, you may have been approaching this wrong. I've made many items for friends using synergy. They must have synergy unlocked, they claim the furnace, they trade the items. I then do the crafting and they can collect the item at the end.