I want to raise my enchanting from Lv.73 to 100 as fast as I can. Does it matter what enchantment or soulgem I use for it?

i think it does but im not sure, though it can't hurt to get some extra power/coin so use grand souls (Like the black star or grand soulgems)

No effect on XP, just value of the enchantment. For max XP, get the Mage stone and rest before starting. That can give you a 35% boost in XP.

Best you can do is have the Mage Stone, Lovers Stone, and Lovers Comfort together.

Soul Gem size or enchantment doesn't matter.

Soul gem size and enchantment does matter...the more powerful the enchantment the more xp you get...

Yeah, unlike with other crafting skills, the price of the finished item does not affect skill increase. So always use petty gems, unless you're making something you plan to use yourself.

No it does not.