The colors on the snake pulled from the cliff in the film are black bands with white edges, surrounded by large regions of red. Therefore this snake is indeed intended to be a poisonous coral snake (not a king snake), possibly the Central American Coral Snake (Micrurus nigrocinctus), which is found in the Caribbean area. Several other species have the same color pattern, though, and the snake shown in the film appears to have larger regions of red than Micrurus nigrocinctus.
One IMDb user reports that the large,
light yellow snake hanging from a beam inside the doorway of Tia's shack
is an albino Burmese python (Python molurus bivittatus).

albino Python molurus bivittatus

Tia's python is seen to the right of the doorway.
One IMDb user reports that the prison dog does not look like a purebred. It appears to be a mutt (= mix), with possibly terrier in it, even though it is large for a terrier.

the Prison Dog in the first film
Cotton's bird is a macaw, a specific type a parrot. It has blue wings, a blue head, a green patch on top of its head, and a yellow front, all of which identify it as a Blue and Gold Macaw (Ara ararauna). The book describes the bird as a "parrot" but the film refers to it only as a "bird."
The serrated sword held in front of Bootstrap to restain him is the sword of a sawfish. These can often be obtained in shell & curio shops. There are multiple species of sawfish.
According to the Triva [8-3-06] section on IMDb's page for the first film, Barbossa's monkey is a capuchin monkey. (Actually, two different capuchin monkeys were used for that film.) There are different species of capuchin monkeys. The monkey in the film has a white face and brown fur beyond its facial region, so it could be a White-Fronted Capuchin (Cebus albifrons).

Barbossa and his monkey
Created: July 13, 2006
Updated: April 19, 2007