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This is part of a review published in April 2008 [Cruise.co.uk] on the Balmoral and the reviewer states "We used the Palms Cafe for buffet breakfasts and lunches and found the choice of food good and to our taste. There was a reasonable number of tables for two and a much appreciated station in the corner of this cafe where complimentary good quality tea/coffee was available all day in addition to similar facilities within cabins. "
So it looks as though you will enjoy tea/coffee in your cabin.
Yes, there are tea/coffee-making facilities in all cabins.