1) 놓다 and 두다 are synonyms when they mean "put" or "place", but they both have other derived meanings too.
- 놓다: 1) put, place, 2) release, let go. 잡은 손을 놓다 (let go of the hand grip).
- 두다: 1) put, place, 2) have (as as part of a family, organization, etc). 뉴욕에 지사를 두다 (has a branch in New York).
2)
- 놓이다: be placed (passive of 놓다). 책상 위에 책이 한 권 놓여 있다 (There's a book (placed) on the table).
- 눕히다: lay someone down (causative of 눕다, "lie down"). 아이를 침대에 눕혔다 (I laid the child on the bed).
3)
- 속다(vi): be deceived, be taken in.
- 속이다(vt): deceive; trick (causative of 속다).
- 숨다(vi): hide from view.
- 숨기다(vt): hide something/someone from view. (causative of 숨다).
Passive and causative verbs in Korean are quite varied in form and the usage pattern can get complex.
There are ~이다, ~히다, ~기다 as you mentioned, and some of them can make both passive and causative verbs.
There are also helper verbs that handle these functions: ~아/어 지다(passive) and ~게 하다(causative).
A lot depends on the meaning of the base verb. For example, 속다 implies passivity (it's never intentional), so there is no separate passive form and 속이다 is only a causative verb. 놓다 on the other hand is a transitive verb with a sense of doing something to an object(that is, causative), so 놓이다 has the passive meaning..
In some cases, the same stem form can function as both passive and causative depending on the context.
For example, for the verb 안다 (to hug or cuddle). 안기다 can mean both "to be hugged/cuddled"(passive) and "to put someone in another person's arms"(causative).
1. 아이는 엄마한테 가서 안겼다 - The child went and put himself in his mother's arms.
2. 언니는 아이를 할머니 품에 안겼다 - Sister put the child in the arms of grandma.
* In English, same transitive verb is used, but in Korean (1) is passive (there's no object), and (2) causative.
So there is no simple rule about them. You'll have to learn them as they come, and at some point it'll get easier.