The phrasal verb 'Pull out' and Think versus Believe

[Jesus1]

Hi! I am afraid I adore asking!

My questions:

1.- Can I use the phrasal verb ?pull out?

in the following imperative to mean
'take your heart out
of your body!'?

E.X Pull your heart out!

I am a little bit confused between pull out
and pull up.

2.- believe versus think. I know what they mean
but sometimes I hesitate which one to choose.
They are so similar!

My examples are:

a.- A deathly silence makes me think/believe
there?s no life in this kind of prison
where I live.

b.- The way you look at me makes me
think/believe you?re telling a lie.

Thanks a lot!

Jes?s

[Tom]

[Yankee]