In the following sentences, are the pairs of prepositions 와/과 and 에게, 을/를 and 에게 correct and completely interchangeable, right?

Question

I have sentence as follows:

저는 친구들과 연락을 해요 and 저는 친구들에게 연락을 해요 (I'm in touch with my friends)

나는 친구들을 도와줬어요 and 나는 친구들에게 도와줬어요 (I helped my friends)

In this sentences, are the pairs of prepositions 와/과 and 에게, 을/를 and 에게 correct and completely interchangeable, right?

Answer 1

To answer the "correct and completely interchangeable" part of your question, no, not completely.

1. 저는 친구들과 연락을 해요 = I keep in touch with my friends.
2. 저는 친구들에게 연락을 해요 = I get in touch with my friends (i.e. contact them).

The two phrases are used interchangeably in many cases, but their main point is a little different. 와/과 연락해요 sounds like two way interaction while 에게 fits one way communication better (might be a small difference but it often matters). So if you're notifying your friend about something, you should use 에게 (e.g. 친구한테/에게 올 필요(가) 없다고 연락했다 / 말했다. 친구와 is strange). Likewise, if you're contacting the police, you don't say 경찰과 연락했다 but must say 경찰에 연락했다 (use 에 instead of 한테/에게 if the recipient is an organization). 경찰과 연락했다 is not completely wrong but it is a much poorer choice.

1. 나는 친구들을 도와줬어요 = I helped my friends.
2. 나는 친구들에게 도와줬어요 (X). This is wrong.

도와주다 is a transitive verb taking a direct object. You can sometimes omit the object but cannot use 에게 in place of 을/를. It sounds strange.

You can correlate the usage with English.

1. 친구를 돕다 / 도와주다 = help a friend.
2. 친구에게 돕다 / 도와주다 (X) = help to a friend (X)
3. 친구에게 도움을 주다 (O) = provide/give help to a friend (O).
4. 동생이 숙제하는 것을 도와주다 = help my brother with his home work. (the structures don't match up in this case)

#3 uses 에게 because the verb is now 주다 which commonly takes P-에게 N-을 주다 (give N to P). 도와주다 is closer to 돕다 in meaning and grammar, so it can't conjugate like 주다.