座る and 腰掛ける: seats and sitting positions
Compare sitting on a floor and on a chair, without overinterpreting posture where 座る and 腰掛ける overlap.
Specify where to sit
こちらの椅子に座ってください。 asks someone to sit on this chair. 座る, read すわる, takes に for the seat and has the te-form 座って.
床に座って、荷物を整理しました。 says that someone sat on the floor and organized their belongings. 座る is not restricted to sitting on a chair.
Take a seat on a chair or bench
ベンチに腰掛けて、友達を待ちました。 says that someone sat on a bench and waited for a friend. 腰掛ける, read こしかける, is used for taking a seat on a support such as a chair.
椅子に浅く腰掛けました。 describes sitting toward the front of a chair. 浅く specifies the shallow position; 腰掛ける alone does not always mean perching on the very edge.
Sitting down and remaining seated
入口の近くに座っている人が案内係です。 identifies the seated person near the entrance as the guide. 座っている describes the state after sitting down.
Both ベンチに座る and ベンチに腰掛ける are possible. Whether the person sits on the ground or a raised support, and whether posture is specified, helps guide the choice.
Does 腰掛ける alone establish that someone sat shallowly on the edge of a chair?
Show the answer and why
No. Add a modifier such as 浅く腰掛ける to specify that position. 腰掛ける can also describe ordinary sitting on a bench.