That cross-stroke creates random eddies in the coffee and effect proper mixing of the cream or sugar, or atleast stirs up the sediments. Finally the removal. The spoon should be tapped lightly on the rim of the mug, two or three times to knock off any large drops. DO NOT lick spoon to remove final drops. Spoon will leave a stain whereever you place it, so place it accordingly.
Companionship is the most overlooked part of drinking coffee.
At its finest coffee is never consumed alone. However the proper companion is important. They should not talk too much, nor require that you talk too much. Talking limits one's ability to savour the moment and the brew. If silences are embarrasing between you and someone, do not drink coffee with them.