1 No - your current sentence is ungrammatical. You probably should use because instead of cause

The main reason I need an extension is because the literature survey took so long.

If you want to keep the word cause, you can use the slightly more stilted

The lengthy literature survey caused me to need an extension.

2 Use of the word cause is given in the dictionary:

Cause Noun

 

A person or thing that gives rise to an action, phenomenon, or condition.

 

Verb

 

Make (something) happen: "this disease can cause blindness".

1 No - your current sentence is ungrammatical. You probably should use because instead of cause

The main reason I need an extension is because the literature survey took so long.

If you want to keep the word cause, you can use the slightly more stilted

The lengthy literature survey caused me to need an extension.

2 Use of the word cause is given in the dictionary:

Cause Noun

A person or thing that gives rise to an action, phenomenon, or condition.

Verb

Make (something) happen: "this disease can cause blindness".