A. Yes. If it is an active sentence, the verb phrase is 'has/have been' in present perfect.
B. For a week means one week period of time, from now back 1 week.
In thes cases we usually use present perfect continuous, however, 'to be' is never put in this tense.
Put it in present perfect.
"Mary is ill for a week" is present tense. We do not use present tense when something happens for a period of time.