Como Barbossa vem a saber que Calypso está preso na carne mortal de Tia Dalma?

Porque ela fez uma barganha com ele. Citando a Wikia :

By the time the Black Pearl reached the coast of Shipwreck Island, Barbossa stood on the ship's forecastle, conversing with Tia Dalma, regarding their bargain. The mystic accused him on intending to betray her and therefore reminded him on that he was brought back from the dead by her power, and also, demonstrating her abilities by briefly decomposing Barbossa's right hand, cautioning him of his fate should he fail to keep his end of the bargain. Barbossa in turn reminded her that she, secretly the goddess Calypso, was the one who needed him; she resurrected Barbossa so he could help retrieve Jack Sparrow from Davy Jones' Locker and summon a meeting of the Brethren Court, since only the nine Pirate Lords had the power to free Calypso. To avoid the risk of the goddess reaching an accord with someone else, Barbossa ordered Pintel and Ragetti to lock Tia Dalma in the brig. Barbossa remained on deck, glancing at his right hand while contemplating his debt.

A Wikia também fornece o diálogo relevante:

Barbossa: "I do not renege on a bargain once struck. But we agreed on ends only. The means are mine to decide."

Calypso: "Caution, Barbossa. Do not forget it was by my power you return from the dead. Or what it mean if you fail me."

Barbossa: "Don't you forget why you had to bring me back. Why I could not leave Jack to his well-deserved fate. It took nine Pirate Lords to bind you, Calypso. And it'll take no less than nine to set you free."

Apesar de ser honesto a mesma página da Wikia contradiz um pouco isso em um parágrafo anterior:

With the death of Hector Barbossa, the Pirate Lord of the Caspian Sea, came a prime opportunity. Tia Dalma/Calypso needed all the Pirate Lords in order to assemble the Brethren Court, so they could release her from her human bonds. And so, through undetermined circumstances, she resurrected Barbossa from the dead and tricked him to summon a meeting of the Brethren and retrieve Jack Sparrow, who was taken to Davy Jones' Locker by the Kraken.

Parece estranho que ela tivesse que enganar Barbossa para fazer o que ela precisava, quando sua tarefa era bem específica: resgatar Jack Sparrow e reunir todos os Lordes do Pirata.

Assim, as circunstâncias exatas de seu acordo permanecem sem solução.

Por que os outros Pirate Lords não a reconheceram também parece ser um furo de trama. Calypso não parece ter poderes para mudar sua aparência, então seu disfarce como Tia Dalma parece frágil.

Até onde Barbossa reconhece Tia Dalma, seu acordo para trazê-lo de volta parece cobrir esse aspecto da história.

Por que os outros senhores piratas não a reconhecem parece ser mais facilmente esclarecida por uma citação de São Feng para Barbossa.

Feng - "The Court has not met in my lifetime."

Barbossa - "Nor mine."

Feng - "And when last it did, my father told me, it ended...badly."

E, de acordo com a wikia :

The First Court consisted of the Nine Pirate Lords who bound the sea goddess Calypso in her human form, on the instruction of Davy Jones, who revealed them secrets from the Journal of the Ancient Seas. They sealed Calypso's fate with Nine Pieces of Eight, so that the rule of the seas would belong to men. The Brethren would convene a further three times before Calypso's eventual release.