I'm really glad that Blizzard recently redid the card artwork to make class-restricted minions more easy to pick out, but I still had some questions. For example, if I'm playing as the warrior, Garrosh Hellscream, am I able to play Alliance minions such as Goldshire Footman? Also, what about minions designated as Pet? Are they hunter-only?
Yes if you're playing as Garrosh you can still play an Alliance minion and vice versa. One example is in the Warrior vs Paladin fireside duel when Uther (an alliance hero) can summon Cairne Bloodhoof ( a "Horde" minion). There is no faction restriction on cards like there is class restrictions.
Now for the Pet thing some Pets like King Krush are hunter specific, while other pets like King Mukla are not and can be used by any class.