What does Jesus mean by, "Again, I leave the world and
go to the Father" (John 16:28)?
He is talking about His forthcoming ascension to heaven.
Do the disciples already understand things even before
the Holy Spirit comes to them as Jesus promised?
Despite their boisterous claim above, their actions in the next few hours will prove them to have understood not
all that much.
Doesn't Jesus say in John 16:31 that they do believe?
Actually He questions it, and tells them that they are about to scatter and desert Him.
What does "the world" (John 16:33) have in store for
Jesus' followers?
"Tribulation" (John 16:33).
How are Christians to deal with it?
Instead of panicking, "have peace" (John 16:33)
since Jesus knew and warned us about it in advance. The sinful world led by
Satan gets more and more sinful, but Jesus has "overcome
the world" (John 16:33), so we know how things end: Satan will be
"cast into the lake of fire" (Revelation 20:10)
to burn for the rest of eternity, while we spend it in heaven with Jesus, so
we should "be of good cheer" (John 16:33).