Sometimes I was thinking whether what disciples wrote down is correct or not. Did they remember what Jesus said when He’s still with them?

The answer should be YES. Firstly, let’s take a look at John 2.

John 2:19
Jesus answered and said to them, Destroy this temple, and in three days I will raise it up.
John 2:20
Then the Jews said, This temple was built in forty-six years, and You will raise it up in three days?
John 2:21
But He spoke of the temple of His body.
John 2:22
When therefore He was raised from the dead, His disciples remembered that He had said this, and they believed the Scripture and the word which Jesus had spoken.

In the above verses we see that the disciples did remember what He has said. But is it possible for them to remember every important words Jesus said? I don’t think they would have notebooks and pen with them at any time. So let’s take a look at John 14.

John 14:25
These things I have spoken to you while abiding with you;
John 14:26
But the Comforter, the Holy Spirit, whom the Father will send in My name, He will teach you all things and remind you of all the things which I have said to you.

Thank the Lord for the Holy Spirit! The Spirit will remind us of all the things.