Yesterday, I reviewed manya lot of words.

'I reviewed a lot of words yesterday'
'I reviewed loads of words yesterday' - more casual
'Yesterday, I went over some vocabulary terms'
'Yesterday I did some vocabulary revision.'

I want to use them in the phrases.

'I want to learn how to use them in phrases' also works.

I learned the terms: 'Each other', 'to be close to' or 'to be close with', 'devastated', 'disappointed', 'the other day', and 'to make a promise'.

I and mMy fiancée and I understand and we close to each othereach other and are very close.

I and my fiancWe made a promise to put hand to handour heads together and think our dreams and our future.

'put hand to hand' doesn't mean anything. 'Put our heads together' means to plan or figure something out together.
Also as you have recently mentioned 'My fiancèe and I' you would just write 'We'.

I'm close withto my fiancée, he is a good person and polite.

I think 'Close to' sounds more romantic! 'Close with' is more friendly.

'I'm close to my fiancée, he is a good person and very polite'. I don't know why but 'very' makes it sound better here! :)

Malika is going through a lot, because ishe's getting a divorce.

'as she's getting a divorce' might sound a bit better!
Malika is going through a lot right now, as she is getting a divorce.

She is totally/completely/absolutely devastated.

Malilka is disappointed, as she is getting a divorce.

I makde myself a promise, to never think about the past.

I promised myself never to think about the past.
I made a promise to myself, never to think about the past

,never to get caught up in the past.

I should think about my future (instead).

I should plan for my future instead.
I have to think about my future instead.