1. Who was Ace the Bat-Hound's original master?
Bat-Hound's original master was John Wilker, an engraver who had been kidnapped by criminals planning to force him to create phony bonds.
2. Superboy's dog, Krypto, joined an organization of super-powered dogs. What were the initials of the organization, and what did they stand for?
Krypto joined the SCPA, the Space Canine Patrol Agents, in Superboy #132.
3. What gave Streaky, Supergirl's cat, its super-powers?
Streaky got its superpowers from X-Kryptonite, a variant of Kryptonite that Supergirl created while experimenting in an effort to eliminate the weakness to Green K that she and Superman were afflicted with.
4. Supergirl also had a pet horse with super abilities named Comet. What famed sorceress gave him his powers?
Comet was given his powers by Circe, in part to atone for a mistake she made in turning him into a horse (he was originally a centaur). Comet was arguably the most powerful creature in the DC universe during the Silver Age of Comics; he had all the powers of Superman and Supergirl, with no vulnerability to Kryptonite.
5. What was the name of the Martian Manhunter's pet dog?
The Martian Manhunter's pet dog was known as Jupiter during his only appearance in Detective #232.
Dan M and Michael Rebain got the first four; Michael Sensei chipped in the answer to the last question (and I suspect knew the other answers as well).