1. "You have just hurt her by saying it." 2. "You're my favourite person for always." Do these two sound natural?

Answer 1

Favourite answer

"that" would be more common in the first sentence.

The second is fine if you are texting or writing it in a card. The more formal way would be "You will always be my favourite person." 

Answer 2

No, honestly. I'd say:

1. You've just hurt her by saying that.

2. You'll always (or forever) be my favourite person.