You need to use the crystal skull in your inventory, or assign it to a hotkey, in order to summon the creature. It is independent of the summoning skills, so you can have the creature and one summon active at the same time.
Any creature parts, potion and enchantment formula that the necromancer, alchemist and enchanter have before you get the battle tower will be available to the respective servants afterwards. There is no need to hold on to any parts or formula until you have the tower.
As long as you have not gotten Naberius to work on your creature, you may want to sort through the parts you have collected, and sell all but the best of each type.
Since you didn't mention the alchemist, the first available is in the starting town in Broken Valley, in the cellar of the miller's house.
