Is "iawn" not translated the same as "very"?
For instance, am I unable to say, "Dw i iawn wedi blino heddiw"?
Iawn is used in several different ways depending in the context. Look at the examples in the www.gweiadur.com dictionary.
You could say Dw i wedi blino iawn, but people also tend to use the phrase Dw i wedi blino'n lân or similar, an idiom meaning 'I'm tired out'.
Why is "Right, thank you." not a proper answer?
That would sound odd here, in the context of an answer to a greeting such as 'How are you?'