靴 and 靴下: putting on shoes and socks
Distinguish two items that share a wearing verb and follow their order.
Putting on shoes
靴 (くつ) means shoes. 「靴を履きました」 means putting shoes on; 履く is read はく.
「玄関で靴を脱ぎました」 says the speaker took shoes off at the entrance. で gives the location of the action.
Socks and their place
靴下 (くつした) means socks. 「靴下を履いてから靴を履きます」 places putting on socks before putting on shoes.
「靴下に穴が開いています」 describes a hole in a sock. Do not change the affected item to a shoe.
Pairs and size
「靴を一足買いました」 means buying a pair of shoes. 一足 (いっそく) here counts a pair, not one shoe.
「靴下は合いますが、靴は小さいです」 says the socks fit but the shoes are small. Items worn on the same feet can receive different fit evaluations.
Does 「靴を一足買いました」 mean buying only one shoe?
Show the answer and why
No. In this context it means one pair.