Translation:My second dog is black.
Could you use "deuxième" instead of "second"
Absolutely, "deuxième" and "second" are strictly synonymous.
Isn't second only used if there is a particular amount of sth.? Like "la second guerre mondiale".
No, there is only one expression I can think of, where "deuxième" cannot replace "seconde", it is to refer to the 1st year in highschool: "la seconde"