French language Q&A Forum

The quiz asked: How would you tell your friends to have faith? "____ confiance, mes amis!" Have faith, my friends.

I answered "Faites" but it wanted "Ayez". Nearly all lessons here that refer to "confiance" associate it with "faire" - not "avoir". There does not seem to be one specifically on "Have faith". What is the grammar rule here?

In the quiz "aime vraiment" was marked wrong and "aime beaucoup" was required. 

As far as I can tell both are equally valid and in common use, even though this lesson does not mention "aime vraiment". And from a literal point of view, since the English said "really like" and not "like a lot" "aime vraiment" seems more appropriate.

Could someone kindly elaborate on the grammatical structure behind instances when ‘ne’ and ‘pas’ occur side-by-side, like ‘Tu peux ne pas venir’ and ‘Prière de ne pas déranger’ please?