川 and 池: rivers and ponds
Distinguish bodies of water from the locations of activities around them.
A flowing watercourse
川 (かわ) means river or stream. 「川に沿って歩きました」 describes walking along the river.
「川を渡りました」 means crossing the river. Walking along it differs from moving to the opposite side.
A pond
池 (いけ) means pond. 「庭に小さな池があります」 locates a small pond in the garden.
「池の周りを歩きました」 means walking around the pond. It does not describe walking through the water.
Where the action occurs
「川で泳ぎました」 means swimming in the river. 「川の近くで休みました」 means resting near it, a different location scope.
「池の水が減りました」 says the amount of water in the pond decreased. It does not say the pond itself ceased to exist.
Does 「池の周りを歩きました」 mean walking in the water?
Show the answer and why
No. It describes a route around the pond.