我相信世界上有外星人存在既英文點講?

Wrong: I believe that there must be alien on the world.
Right: I believe (that) there must be aliens in the world.

Wrong: I believed there are aliens exist in this world.
Right: I believe there are aliens in this world. OR I believe aliens exist in this world. It cannot be I believeD (past tense), unless you don't believe in it anymore.

Right: I believe that there are aliens in the world
Right: I believe that there are aliens living in the world.

Wrong: What I blieve is that there are alines living in the world.
Right: What I believe is that there are aliens living in the world. (Just a few typos... However, this is a clumsy way to put it. It's just so much more direct to say 'I believe...')

Wrong: I believe there are extra terrestrials exist in this world.
Right: I believe there are extra-terrestrials in this world. OR I believe extra-terrestials exist in this world.


Another way to put it:
I believe in the existence of aliens / extra-terrestrials.

I believe there are extra terrestrials exist in this world.

extra terrestrial - E.T. 外太空生物，外星人
exist - 生存 ，存在

I believe that there are aliens in the world

I believed there are aliens exist in this world.

I believe that there must be alien on the world.