He stayed a week
vs
He stayed for a week

I would say that just’a week’ would be more casual, and something you would speak, whereas’for a week’is more formal (and grammatically correct) & would prbably be written. However here I would say that the diference is more or less negligible.

I consider her a friend,
I
consider her a friend.

I would use the phrase ‘I consider her my friend’.

I consider her as my friend. This sounds odd to me. I wouldn’t use that. In one instance I might use the latter could be in the case of emphasis or speaking the sentense slow or angrily.

I don’t know whether he can be called
and
I don’t know whether he can be called

a messenger or not. They are identical (in terms of interchangeability and naturalness) and I hate

them both.