You can improve with raw leather that has lower quality than the item you are improving however you will suffer from larger fail to improve rates.
The only item used that has its own skill is a mallet; the miscellaneous skill “hammer” will effect affect your ability to successfully improve with the mallet.
As with other skills you will gain the most skill by improving items rather than creating them, and when the item quality is closer to your skill you will also gain the most skill. Working on drake armour gives a greater skill gain than plain or studded leather armour.